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  Subjects -> BUSINESS AND ECONOMICS (Total: 3070 journals)
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BUSINESS AND ECONOMICS (1145 journals)                  1 2 3 4 5 6 | Last

Showing 1 - 200 of 1566 Journals sorted alphabetically
4OR: A Quarterly Journal of Operations Research     Hybrid Journal   (Followers: 9)
Abacus     Hybrid Journal   (Followers: 12)
Accounting Forum     Hybrid Journal   (Followers: 22)
Acta Amazonica     Open Access   (Followers: 3)
Acta Commercii     Open Access   (Followers: 2)
Acta Oeconomica     Full-text available via subscription   (Followers: 2)
Acta Scientiarum. Human and Social Sciences     Open Access   (Followers: 4)
Acta Universitatis Danubius. Œconomica     Open Access  
Acta Universitatis Nicolai Copernici Zarządzanie     Open Access   (Followers: 3)
AD-minister     Open Access   (Followers: 2)
ADR Bulletin     Open Access   (Followers: 5)
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AfricaGrowth Agenda     Full-text available via subscription   (Followers: 1)
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African Journal of Business Ethics     Open Access   (Followers: 7)
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Afro-Asian Journal of Finance and Accounting     Hybrid Journal   (Followers: 6)
Afyon Kocatepe Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi     Open Access   (Followers: 3)
Agronomy     Open Access   (Followers: 11)
Akademika : Journal of Southeast Asia Social Sciences and Humanities     Open Access   (Followers: 4)
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Annales de l'Institut Henri Poincare (C) Non Linear Analysis     Full-text available via subscription   (Followers: 1)
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Arab Economic and Business Journal     Open Access   (Followers: 3)
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Argomenti. Rivista di economia, cultura e ricerca sociale     Open Access   (Followers: 2)
ASEAN Economic Bulletin     Full-text available via subscription   (Followers: 5)
Asia Pacific Business Review     Hybrid Journal   (Followers: 5)
Asia Pacific Journal of Human Resources     Hybrid Journal   (Followers: 322)
Asia Pacific Viewpoint     Hybrid Journal   (Followers: 1)
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Asian Development Review     Open Access   (Followers: 14)
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Asian Economic Papers     Hybrid Journal   (Followers: 7)
Asian Economic Policy Review     Hybrid Journal   (Followers: 4)
Asian Journal of Accounting and Governance     Open Access   (Followers: 3)
Asian Journal of Business Ethics     Hybrid Journal   (Followers: 7)
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Asian Journal of Technology Innovation     Hybrid Journal   (Followers: 8)
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Australian Economic Papers     Hybrid Journal   (Followers: 21)
Australian Economic Review     Hybrid Journal   (Followers: 7)
Australian Journal of Maritime and Ocean Affairs     Hybrid Journal   (Followers: 10)
Balkan Region Conference on Engineering and Business Education     Open Access   (Followers: 1)
Baltic Journal of Real Estate Economics and Construction Management     Open Access   (Followers: 1)
Banks in Insurance Report     Hybrid Journal   (Followers: 2)
BBR - Brazilian Business Review     Open Access   (Followers: 4)
Benchmarking : An International Journal     Hybrid Journal   (Followers: 11)
BER : Consumer Confidence Survey     Full-text available via subscription   (Followers: 4)
BER : Economic Prospects : An Executive Summary     Full-text available via subscription  
BER : Economic Prospects : Full Survey     Full-text available via subscription   (Followers: 2)
BER : Intermediate Goods Industries Survey     Full-text available via subscription   (Followers: 1)
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BER : Motor Trade Survey     Full-text available via subscription   (Followers: 1)
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BER : Survey of Business Conditions in Building and Construction : An Executive Summary     Full-text available via subscription   (Followers: 4)
BER : Survey of Business Conditions in Manufacturing : An Executive Summary     Full-text available via subscription   (Followers: 3)
BER : Survey of Business Conditions in Retail : An Executive Summary     Full-text available via subscription   (Followers: 3)
BER : Trends : Full Survey     Full-text available via subscription   (Followers: 2)
BER : Wholesale Sector Survey     Full-text available via subscription   (Followers: 1)
Berkeley Business Law Journal     Free   (Followers: 11)
Bio-based and Applied Economics     Open Access   (Followers: 1)
Biodegradation     Hybrid Journal   (Followers: 1)
Biology Direct     Open Access   (Followers: 7)
Black Enterprise     Full-text available via subscription  
Board & Administrator for Administrators only     Hybrid Journal  
Border Crossing : Transnational Working Papers     Open Access   (Followers: 2)
Briefings in Real Estate Finance     Hybrid Journal   (Followers: 5)
British Journal of Industrial Relations     Hybrid Journal   (Followers: 30)
Brookings Papers on Economic Activity     Open Access   (Followers: 47)
Brookings Trade Forum     Full-text available via subscription   (Followers: 3)
BRQ Business Research Quarterly     Open Access   (Followers: 2)
Building Sustainable Legacies : The New Frontier Of Societal Value Co-Creation     Full-text available via subscription   (Followers: 1)
Bulletin of Economic Research     Hybrid Journal   (Followers: 16)
Bulletin of Geography. Socio-economic Series     Open Access   (Followers: 7)
Bulletin of Indonesian Economic Studies     Hybrid Journal   (Followers: 3)
Bulletin of the Dnipropetrovsk University. Series : Management of Innovations     Open Access   (Followers: 1)
Business & Entrepreneurship Journal     Open Access   (Followers: 16)
Business & Information Systems Engineering     Hybrid Journal   (Followers: 5)
Business & Society     Hybrid Journal   (Followers: 9)
Business : Theory and Practice / Verslas : Teorija ir Praktika     Open Access   (Followers: 1)
Business and Economic Research     Open Access   (Followers: 6)
Business and Management Horizons     Open Access   (Followers: 11)
Business and Management Research     Open Access   (Followers: 17)
Business and Management Studies     Open Access   (Followers: 9)
Business and Politics     Hybrid Journal   (Followers: 6)
Business and Professional Communication Quarterly     Hybrid Journal   (Followers: 7)
Business and Society Review     Hybrid Journal   (Followers: 5)
Business Economics     Hybrid Journal   (Followers: 6)
Business Ethics: A European Review     Hybrid Journal   (Followers: 16)
Business Horizons     Hybrid Journal   (Followers: 8)
Business Information Review     Hybrid Journal   (Followers: 13)
Business Management and Strategy     Open Access   (Followers: 40)
Business Research     Hybrid Journal   (Followers: 2)
Business Strategy and the Environment     Hybrid Journal   (Followers: 12)
Business Strategy Review     Hybrid Journal   (Followers: 7)
Business Strategy Series     Hybrid Journal   (Followers: 6)
Business Systems & Economics     Open Access   (Followers: 2)
Business Systems Research Journal     Open Access   (Followers: 5)
Business, Management and Education     Open Access   (Followers: 17)
Business, Peace and Sustainable Development     Full-text available via subscription   (Followers: 3)
Bustan     Hybrid Journal   (Followers: 1)
Cadernos EBAPE.BR     Open Access   (Followers: 1)
Cambridge Journal of Economics     Hybrid Journal   (Followers: 55)
Cambridge Journal of Regions, Economy and Society     Hybrid Journal   (Followers: 9)
Canadian Journal of Administrative Sciences / Revue Canadienne des Sciences de l Administration     Hybrid Journal   (Followers: 1)
Canadian Journal of Economics/Revue Canadienne d`Economique     Hybrid Journal   (Followers: 25)
Canadian journal of nonprofit and social economy research     Open Access   (Followers: 2)
Capitalism and Society     Hybrid Journal   (Followers: 2)
Capitalism Nature Socialism     Hybrid Journal   (Followers: 11)
Case Studies in Business and Management     Open Access   (Followers: 8)
CBU International Conference Proceedings     Open Access   (Followers: 1)
Central European Journal of Operations Research     Hybrid Journal   (Followers: 5)
Central European Journal of Public Policy     Open Access   (Followers: 1)
CESifo Economic Studies     Hybrid Journal   (Followers: 15)
Chain Reaction     Full-text available via subscription  
Challenge     Full-text available via subscription   (Followers: 4)
China & World Economy     Hybrid Journal   (Followers: 15)
China : An International Journal     Full-text available via subscription   (Followers: 16)
China Economic Journal: The Official Journal of the China Center for Economic Research (CCER) at Peking University     Hybrid Journal   (Followers: 10)
China Economic Review     Hybrid Journal   (Followers: 10)
China Finance Review International     Hybrid Journal   (Followers: 5)
China Nonprofit Review     Hybrid Journal   (Followers: 3)
China perspectives     Open Access   (Followers: 11)
Chinese Economy     Full-text available via subscription  
Ciência & Saúde Coletiva     Open Access   (Followers: 2)
CLIO América     Open Access   (Followers: 1)
Cliometrica     Hybrid Journal   (Followers: 1)
COEPTUM     Open Access  
Community Development Journal     Hybrid Journal   (Followers: 23)
Compensation & Benefits Review     Hybrid Journal   (Followers: 6)
Competition & Change     Hybrid Journal   (Followers: 10)
Competitive Intelligence Review     Hybrid Journal   (Followers: 2)
Competitiveness Review : An International Business Journal incorporating Journal of Global Competitiveness     Hybrid Journal   (Followers: 5)
Computational Economics     Hybrid Journal   (Followers: 9)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computer Law & Security Review     Hybrid Journal   (Followers: 15)
Computers & Operations Research     Hybrid Journal   (Followers: 10)
Construction Innovation: Information, Process, Management     Hybrid Journal   (Followers: 14)
Contemporary Wales     Full-text available via subscription   (Followers: 3)
Contextus - Revista Contemporânea de Economia e Gestão     Open Access   (Followers: 1)
Contributions to Political Economy     Hybrid Journal   (Followers: 6)
Corporate Communications An International Journal     Hybrid Journal   (Followers: 5)
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Creative and Knowledge Society     Open Access   (Followers: 10)
Creative Industries Journal     Hybrid Journal   (Followers: 8)
CRIS - Bulletin of the Centre for Research and Interdisciplinary Study     Open Access   (Followers: 1)
Crossing the Border : International Journal of Interdisciplinary Studies     Open Access   (Followers: 4)
Cuadernos de Administración (Universidad del Valle)     Open Access   (Followers: 1)
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Cuadernos de Economia - Latin American Journal of Economics     Open Access   (Followers: 1)
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Current Opinion in Creativity, Innovation and Entrepreneurship     Open Access   (Followers: 8)
De Economist     Hybrid Journal   (Followers: 12)
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Decision Support Systems     Hybrid Journal   (Followers: 15)
Defence and Peace Economics     Hybrid Journal   (Followers: 16)
der markt     Hybrid Journal   (Followers: 1)
Desenvolvimento em Questão     Open Access  
Development     Full-text available via subscription   (Followers: 23)
Development and Change     Hybrid Journal   (Followers: 47)
Development and Learning in Organizations     Hybrid Journal   (Followers: 7)

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Journal Cover Annales de l'Institut Henri Poincare (C) Non Linear Analysis
  [SJR: 2.558]   [H-I: 46]   [1 followers]  Follow
    
   Full-text available via subscription Subscription journal  (Not entitled to full-text)
   ISSN (Print) 0294-1449
   Published by Elsevier Homepage  [3030 journals]
  • Regularity of the free boundary for the obstacle problem for the
           fractional Laplacian with drift
    • Authors: Nicola Garofalo; Arshak Petrosyan; Camelia A. Pop; Mariana Smit Vega Garcia
      Pages: 533 - 570
      Abstract: Publication date: May–June 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 3
      Author(s): Nicola Garofalo, Arshak Petrosyan, Camelia A. Pop, Mariana Smit Vega Garcia
      We establish the C 1 + γ -Hölder regularity of the regular free boundary in the stationary obstacle problem defined by the fractional Laplace operator with drift in the subcritical regime. Our method of the proof consists in proving a new monotonicity formula and an epiperimetric inequality. Both tools generalizes the original ideas of G. Weiss in [15] for the classical obstacle problem to the framework of fractional powers of the Laplace operator with drift. Our study continues the earlier research [12], where two of us established the optimal interior regularity of solutions.

      PubDate: 2017-04-18T16:14:59Z
      DOI: 10.1016/j.anihpc.2016.03.001
       
  • Global existence for reaction–diffusion systems with nonlinear
           diffusion and control of mass
    • Authors: El Haj Laamri; Michel Pierre
      Pages: 571 - 591
      Abstract: Publication date: May–June 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 3
      Author(s): El Haj Laamri, Michel Pierre
      We prove here global existence in time of weak solutions for some reaction–diffusion systems with natural structure conditions on the nonlinear reactive terms which provide positivity of the solutions and uniform control of the total mass. The diffusion operators are nonlinear, in particular operators of the porous media type u i ↦ − d i Δ u i m i . Global existence is proved under the assumption that the reactive terms are bounded in L 1 . This extends previous similar results obtained in the semilinear case when the diffusion operators are linear of type u i ↦ − d i Δ u i .

      PubDate: 2017-04-18T16:14:59Z
      DOI: 10.1016/j.anihpc.2016.03.002
       
  • The Cauchy–Dirichlet problem for a general class of parabolic
           equations
    • Authors: Paolo Baroni; Casimir Lindfors
      Pages: 593 - 624
      Abstract: Publication date: May–June 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 3
      Author(s): Paolo Baroni, Casimir Lindfors
      We prove regularity results such as interior Lipschitz regularity and boundary continuity for the Cauchy–Dirichlet problem associated to a class of parabolic equations inspired by the evolutionary p-Laplacian, but extending it at a wide scale. We employ a regularization technique of viscosity-type that we find interesting in itself.

      PubDate: 2017-04-18T16:14:59Z
      DOI: 10.1016/j.anihpc.2016.03.003
       
  • On phase separation in systems of coupled elliptic equations: Asymptotic
           analysis and geometric aspects
    • Authors: Nicola Soave; Alessandro Zilio
      Pages: 625 - 654
      Abstract: Publication date: May–June 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 3
      Author(s): Nicola Soave, Alessandro Zilio
      We consider a family of positive solutions to the system of k components − Δ u i , β = f ( x , u i , β ) − β u i , β ∑ j ≠ i a i j u j , β 2 in  Ω , where Ω ⊂ R N with N ≥ 2 . It is known that uniform bounds in L ∞ of { u β } imply convergence of the densities to a segregated configuration, as the competition parameter β diverges to +∞. In this paper we establish sharp quantitative point-wise estimates for the densities around the interface between different components, and we characterize the asymptotic profile of u β in terms of entire solutions to the limit system Δ U i = U i ∑ j ≠ i a i j U j 2 . Moreover, we develop a uniform-in-β regularity theory for the interfaces.

      PubDate: 2017-04-18T16:14:59Z
      DOI: 10.1016/j.anihpc.2016.04.001
       
  • Singularly perturbed equations of degenerate type
    • Authors: Damião J. Araújo; Gleydson C. Ricarte; Eduardo V. Teixeira
      Pages: 655 - 678
      Abstract: Publication date: May–June 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 3
      Author(s): Damião J. Araújo, Gleydson C. Ricarte, Eduardo V. Teixeira
      This work is devoted to the study of nonvariational, singularly perturbed elliptic equations of degenerate type. The governing operator is anisotropic and ellipticity degenerates along the set of critical points. The singular behavior is of order O ( 1 ϵ ) along ϵ-level layers { u ϵ ∼ ϵ } , and a non-homogeneous source acts in the noncoincidence region { u ϵ > ϵ } . We obtain the precise geometric behavior of solutions near ϵ-level surfaces, by means of optimal regularity and sharp geometric nondegeneracy. We further investigate Hausdorff measure properties of ϵ-level surfaces. The analysis of the asymptotic limits as the ϵ parameter goes to zero is also carried out. The results obtained are new even if restricted to the uniformly elliptic, isotropic setting.

      PubDate: 2017-04-18T16:14:59Z
      DOI: 10.1016/j.anihpc.2016.03.004
       
  • A higher dimensional Poincaré–Birkhoff theorem for Hamiltonian
           flows
    • Authors: Alessandro Fonda; Antonio J. Ureña
      Pages: 679 - 698
      Abstract: Publication date: May–June 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 3
      Author(s): Alessandro Fonda, Antonio J. Ureña
      We propose an extension to higher dimensions of the Poincaré–Birkhoff Theorem which applies to Poincaré time-maps of Hamiltonian systems. Examples of applications to pendulum-type systems and weakly-coupled superlinear systems are also given.

      PubDate: 2017-04-18T16:14:59Z
      DOI: 10.1016/j.anihpc.2016.04.002
       
  • J.-L. Lions' problem concerning maximal regularity of equations governed
           by non-autonomous forms
    • Authors: Stephan Fackler
      Pages: 699 - 709
      Abstract: Publication date: May–June 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 3
      Author(s): Stephan Fackler
      An old problem due to J.-L. Lions going back to the 1960s asks whether the abstract Cauchy problem associated to non-autonomous symmetric forms has maximal regularity if the time dependence is merely assumed to be continuous or even measurable. We give a negative answer to this question and discuss the minimal regularity needed for positive results.

      PubDate: 2017-04-18T16:14:59Z
      DOI: 10.1016/j.anihpc.2016.05.001
       
  • On the kinetic energy profile of Hölder continuous Euler flows
    • Authors: Philip Isett; Sung-Jin Oh
      Pages: 711 - 730
      Abstract: Publication date: May–June 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 3
      Author(s): Philip Isett, Sung-Jin Oh
      In [8], the first author proposed a strengthening of Onsager's conjecture on the failure of energy conservation for incompressible Euler flows with Hölder regularity not exceeding 1/3. This stronger form of the conjecture implies that anomalous dissipation will fail for a generic Euler flow with regularity below the Onsager critical space L t ∞ B 3 , ∞ 1 / 3 due to low regularity of the energy profile. The present paper is the second in a series of two papers whose results may be viewed as first steps towards establishing the conjectured failure of energy regularity for generic solutions with Hölder exponent less than 1/5. The main result of this paper shows that any non-negative function with compact support and Hölder regularity 1/2 can be prescribed as the energy profile of an Euler flow in the class C t , x 1 / 5 − ϵ . The exponent 1/2 is sharp in view of a regularity result of Isett [8]. The proof employs an improved greedy algorithm scheme that builds upon that in Buckmaster–De Lellis–Székelyhidi [1].

      PubDate: 2017-04-18T16:14:59Z
      DOI: 10.1016/j.anihpc.2016.05.002
       
  • Long time behavior for a dissipative shallow water model
    • Authors: V. Sciacca; M.E. Schonbek; M. Sammartino
      Pages: 731 - 757
      Abstract: Publication date: May–June 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 3
      Author(s): V. Sciacca, M.E. Schonbek, M. Sammartino
      We consider the two-dimensional shallow water model derived in [29], describing the motion of an incompressible fluid, confined in a shallow basin, with varying bottom topography. We construct the approximate inertial manifolds for the associated dynamical system and estimate its order. Finally, working in the whole space R 2 , under suitable conditions on the time dependent forcing term, we prove the L 2 asymptotic decay of the weak solutions.

      PubDate: 2017-04-18T16:14:59Z
      DOI: 10.1016/j.anihpc.2016.05.003
       
  • The defocusing quintic NLS in four space dimensions
    • Authors: Benjamin Dodson; Changxing Miao; Jason Murphy; Jiqiang Zheng
      Pages: 759 - 787
      Abstract: Publication date: May–June 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 3
      Author(s): Benjamin Dodson, Changxing Miao, Jason Murphy, Jiqiang Zheng
      We consider the defocusing quintic nonlinear Schrödinger equation in four space dimensions. We prove that any solution that remains bounded in the critical Sobolev space must be global and scatter. We employ a space-localized interaction Morawetz inequality, the proof of which requires us to overcome the logarithmic failure in the double Duhamel argument in four dimensions.

      PubDate: 2017-04-18T16:14:59Z
      DOI: 10.1016/j.anihpc.2016.05.004
       
  • Corrigendum to “Analysis of degenerate cross-diffusion population models
           with volume filling” [Ann. Inst. Henri Poincaré 34 (1) (2017) 1–29]
    • Authors: Nicola Zamponi; Ansgar Jüngel
      Pages: 789 - 792
      Abstract: Publication date: May–June 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 3
      Author(s): Nicola Zamponi, Ansgar Jüngel
      This note corrects Lemma 7 in [1] on the positive (semi-)definiteness of a certain matrix product, which yields a priori estimates for the cross-diffusion system.

      PubDate: 2017-04-18T16:14:59Z
      DOI: 10.1016/j.anihpc.2016.06.001
       
  • On the asymptotic behaviour of solutions of the stationary Navier–Stokes
           equations in dimension 3
    • Authors: Agathe Decaster; Dragoş Iftimie
      Pages: 277 - 291
      Abstract: Publication date: March–April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 2
      Author(s): Agathe Decaster, Dragoş Iftimie
      In this paper, we address the problem of determining the asymptotic behaviour of the solutions of the incompressible stationary Navier–Stokes system in the full space, with a forcing term whose asymptotic behaviour at infinity is homogeneous of degree −3. We identify the asymptotic behaviour at infinity of the solution. We prove that it is homogeneous and that the leading term in the expansion at infinity uniquely solves the homogeneous Navier–Stokes equations with a forcing term which involves an additional Dirac mass. This also applies to the case of an exterior domain.

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2015.12.002
       
  • The obstacle problem with singular coefficients near Dirichlet data
    • Authors: Henrik Shahgholian; Karen Yeressian
      Pages: 293 - 334
      Abstract: Publication date: March–April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 2
      Author(s): Henrik Shahgholian, Karen Yeressian
      In this paper we study the behaviour of the free boundary close to its contact points with the fixed boundary B ∩ { x 1 = 0 } in the obstacle type problem { div ( x 1 a ∇ u ) = χ { u > 0 } in B + , u = 0 on B ∩ { x 1 = 0 } where a < 1 , B + = B ∩ { x 1 > 0 } , B is the unit ball in R n and n ≥ 2 is an integer. Let Γ = B + ∩ ∂ { u > 0 } be the free boundary and assume that the origin is a contact point, i.e. 0 ∈ Γ ‾ . We prove that the free boundary touches the fixed boundary uniformly tangentially at the origin, near to the origin it is the graph of a C 1 function and there is a uniform modulus of continuity for the derivatives of this function.

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2015.12.003
       
  • Generic regularity of conservative solutions to a nonlinear wave equation
    • Authors: Alberto Bressan; Geng Chen
      Pages: 335 - 354
      Abstract: Publication date: March–April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 2
      Author(s): Alberto Bressan, Geng Chen
      The paper is concerned with conservative solutions to the nonlinear wave equation u t t − c ( u ) ( c ( u ) u x ) x   =   0 . For an open dense set of C 3 initial data, we prove that the solution is piecewise smooth in the t–x plane, while the gradient u x can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in [7], which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom's transversality theorem.

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2015.12.004
       
  • Parabolic equations and the bounded slope condition
    • Authors: Verena Bögelein; Frank Duzaar; Paolo Marcellini; Stefano Signoriello
      Pages: 355 - 379
      Abstract: Publication date: March–April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 2
      Author(s): Verena Bögelein, Frank Duzaar, Paolo Marcellini, Stefano Signoriello
      In this paper we establish the existence of Lipschitz-continuous solutions to the Cauchy Dirichlet problem of evolutionary partial differential equations { ∂ t u − div D f ( D u ) = 0 in  Ω T , u = u o on  ∂ P Ω T . The only assumptions needed are the convexity of the generating function f : R n → R , and the classical bounded slope condition on the initial and the lateral boundary datum u o ∈ W 1 , ∞ ( Ω ) . We emphasize that no growth conditions are assumed on f and that – an example which does not enter in the elliptic case – u o could be any Lipschitz initial and boundary datum, vanishing at the boundary ∂Ω, and the boundary may contain flat parts, for instance Ω could be a rectangle in R n .

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2015.12.005
       
  • On the attractor for the semi-dissipative Boussinesq equations
    • Authors: Animikh Biswas; Ciprian Foias; Adam Larios
      Pages: 381 - 405
      Abstract: Publication date: March–April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 2
      Author(s): Animikh Biswas, Ciprian Foias, Adam Larios
      In this article, we study the long time behavior of solutions of a variant of the Boussinesq system in which the equation for the velocity is parabolic while the equation for the temperature is hyperbolic. We prove that the system has a global attractor which retains some of the properties of the global attractors for the 2D and 3D Navier–Stokes equations. Moreover, this attractor contains infinitely many invariant manifolds in which several universal properties of the Batchelor, Kraichnan, Leith theory of turbulence are potentially present.

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2015.12.006
       
  • Transience and multifractal analysis
    • Authors: Godofredo Iommi; Thomas Jordan; Mike Todd
      Pages: 407 - 421
      Abstract: Publication date: March–April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 2
      Author(s): Godofredo Iommi, Thomas Jordan, Mike Todd
      We study dimension theory for dissipative dynamical systems, proving a conditional variational principle for the quotients of Birkhoff averages restricted to the recurrent part of the system. On the other hand, we show that when the whole system is considered (and not just its recurrent part) the conditional variational principle does not necessarily hold. Moreover, we exhibit an example of a topologically transitive map having discontinuous Lyapunov spectrum. The mechanism producing all these pathological features on the multifractal spectra is transience, that is, the non-recurrent part of the dynamics.

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2015.12.007
       
  • From constant to non-degenerately vanishing magnetic fields in
           superconductivity
    • Authors: Bernard Helffer; Ayman Kachmar
      Pages: 423 - 438
      Abstract: Publication date: March–April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 2
      Author(s): Bernard Helffer, Ayman Kachmar
      We explore the relationship between two reference functions arising in the analysis of the Ginzburg–Landau functional. The first function describes the distribution of superconductivity in a type II superconductor subjected to a constant magnetic field. The second function describes the distribution of superconductivity in a type II superconductor submitted to a variable magnetic field that vanishes non-degenerately along a smooth curve.

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2015.12.008
       
  • Nonhomogeneous boundary conditions for the spectral fractional Laplacian
    • Authors: Nicola Abatangelo; Louis Dupaigne
      Pages: 439 - 467
      Abstract: Publication date: March–April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 2
      Author(s): Nicola Abatangelo, Louis Dupaigne
      We present a construction of harmonic functions on bounded domains for the spectral fractional Laplacian operator and we classify them in terms of their divergent profile at the boundary. This is used to establish and solve boundary value problems associated with nonhomogeneous boundary conditions. We provide a weak- L 1 theory to show how problems with measure data at the boundary and inside the domain are well-posed. We study linear and semilinear problems, performing a sub- and supersolution method. We finally show the existence of large solutions for some power-like nonlinearities.

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2016.02.001
       
  • A one-dimensional symmetry result for a class of nonlocal semilinear
           equations in the plane
    • Authors: François Hamel; Xavier Ros-Oton; Yannick Sire; Enrico Valdinoci
      Pages: 469 - 482
      Abstract: Publication date: March–April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 2
      Author(s): François Hamel, Xavier Ros-Oton, Yannick Sire, Enrico Valdinoci
      We consider entire solutions to L u = f ( u ) in R 2 , where L is a nonlocal operator with translation invariant, even and compactly supported kernel K. Under different assumptions on the operator L , we show that monotone solutions are necessarily one-dimensional. The proof is based on a Liouville type approach. A variational characterization of the stability notion is also given, extending our results in some cases to stable solutions.

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2016.01.001
       
  • Viscoelastic flows in a rough channel: A multiscale analysis
    • Authors: Laurent Chupin; Sébastien Martin
      Pages: 483 - 508
      Abstract: Publication date: March–April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 2
      Author(s): Laurent Chupin, Sébastien Martin
      We investigate the influence of the rough boundaries on viscoelastic flows, described by the diffusive Oldroyd model. The fluid domain has a rough wall modeled by roughness patterns of size ε ≪ 1 . We present and rigorously justify an asymptotic expansion with respect to ε, at any order, based upon the definition of elementary problems: Oldroyd-type problems at the global scale defined on a smoothened domain and boundary-layer corrector problems. The resulting analysis guarantees optimality with respect to the truncation error and leads to a numerical algorithm which allows us to build the approximation of the solution at any required precision.

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2016.01.002
       
  • On the growth of Sobolev norms of solutions of the fractional defocusing
           NLS equation on the circle
    • Authors: Joseph Thirouin
      Pages: 509 - 531
      Abstract: Publication date: March–April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 2
      Author(s): Joseph Thirouin
      This paper is devoted to the study of large time bounds for the Sobolev norms of the solutions of the following fractional cubic Schrödinger equation on the torus: i ∂ t u = D α u + u 2 u , u ( 0 , ⋅ ) = u 0 , where α is a real parameter. We show that, apart from the case α = 1 , which corresponds to a half-wave equation with no dispersive property at all, solutions of this equation grow at a polynomial rate at most. We also address the case of the cubic and quadratic half-wave equations.

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2016.02.002
       
  • Analysis of degenerate cross-diffusion population models with volume
           filling
    • Authors: Nicola Zamponi; Ansgar Jüngel
      Pages: 1 - 29
      Abstract: Publication date: January–February 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 1
      Author(s): Nicola Zamponi, Ansgar Jüngel
      A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk lattice model in the diffusion limit. Compared to previous results in the literature, the novelty is the combination of general degenerate diffusion and volume-filling effects. Conditions on the nonlinear diffusion coefficients are identified, which yield a formal gradient-flow or entropy structure. This structure allows for the proof of global-in-time existence of bounded weak solutions and the exponential convergence of the solutions to the constant steady state. The existence proof is based on an approximation argument, the entropy inequality, and new nonlinear Aubin–Lions compactness lemmas. The proof of the large-time behavior employs the entropy estimate and convex Sobolev inequalities. Moreover, under simplifying assumptions on the nonlinearities, the uniqueness of weak solutions is shown by using the H − 1 method, the E-monotonicity technique of Gajewski, and the subadditivity of the Fisher information.

      PubDate: 2017-01-13T07:15:50Z
      DOI: 10.1016/j.anihpc.2015.08.003
       
  • Spectral structure of transfer operators for expanding circle maps
    • Authors: Oscar F. Bandtlow; Wolfram Just; Julia Slipantschuk
      Pages: 31 - 43
      Abstract: Publication date: January–February 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 1
      Author(s): Oscar F. Bandtlow, Wolfram Just, Julia Slipantschuk
      We explicitly determine the spectrum of transfer operators (acting on spaces of holomorphic functions) associated to analytic expanding circle maps arising from finite Blaschke products. This is achieved by deriving a convenient natural representation of the respective adjoint operators.

      PubDate: 2017-01-13T07:15:50Z
      DOI: 10.1016/j.anihpc.2015.08.004
       
  • The Monge–Ampère constraint: Matching of isometries, density and
           regularity, and elastic theories of shallow shells
    • Authors: Marta Lewicka; L. Mahadevan; Mohammad Reza Pakzad
      Pages: 45 - 67
      Abstract: Publication date: January–February 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 1
      Author(s): Marta Lewicka, L. Mahadevan, Mohammad Reza Pakzad
      The main analytical ingredients of the first part of this paper are two independent results: a theorem on approximation of W 2 , 2 solutions of the Monge–Ampère equation by smooth solutions, and a theorem on the matching (in other words, continuation) of second order isometries to exact isometric embeddings of 2d surface in R 3 . In the second part, we rigorously derive the Γ-limit of 3-dimensional nonlinear elastic energy of a shallow shell of thickness h, where the depth of the shell scales like h α and the applied forces scale like h α + 2 , in the limit when h → 0 . We offer a full analysis of the problem in the parameter range α ∈ ( 1 / 2 , 1 ) . We also complete the analysis in some specific cases for the full range α ∈ ( 0 , 1 ) , applying the results of the first part of the paper.

      PubDate: 2017-01-13T07:15:50Z
      DOI: 10.1016/j.anihpc.2015.08.005
       
  • Moderate solutions of semilinear elliptic equations with Hardy potential
    • Authors: Moshe Marcus; Phuoc-Tai Nguyen
      Pages: 69 - 88
      Abstract: Publication date: January–February 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 1
      Author(s): Moshe Marcus, Phuoc-Tai Nguyen
      Let Ω be a bounded smooth domain in R N . We study positive solutions of equation (E) − L μ u + u q = 0 in Ω where L μ = Δ + μ δ 2 , 0 < μ , q > 1 and δ ( x ) = dist ( x , ∂ Ω ) . A positive solution of (E) is moderate if it is dominated by an L μ -harmonic function. If μ < C H ( Ω ) (the Hardy constant for Ω) every positive L μ -harmonic function can be represented in terms of a finite measure on ∂Ω via the Martin representation theorem. However the classical measure boundary trace of any such solution is zero. We introduce a notion of normalized boundary trace by which we obtain a complete classification of the positive moderate solutions of (E) in the subcritical case, 1 < q < q μ , c . (The critical value depends only on N and μ.) For q ≥ q μ , c there exists no moderate solution with an isolated singularity on the boundary. The normalized boundary trace and associated boundary value problems are also discussed in detail for the linear operator L μ . These results form the basis for the study of the nonlinear problem.

      PubDate: 2017-01-13T07:15:50Z
      DOI: 10.1016/j.anihpc.2015.10.001
       
  • Everywhere differentiability of viscosity solutions to a class of
           Aronsson's equations
    • Authors: Juhana Siljander; Changyou Wang; Yuan Zhou
      Pages: 119 - 138
      Abstract: Publication date: January–February 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 1
      Author(s): Juhana Siljander, Changyou Wang, Yuan Zhou
      We show the everywhere differentiability of viscosity solutions to a class of Aronsson equations in R n for n ≥ 2 , where the coefficient matrices A are assumed to be uniformly elliptic and C 1 , 1 . Our result extends an earlier important theorem by Evans and Smart [18] who have studied the case A = I n which correspond to the ∞-Laplace equation. We also show that every point is a Lebesgue point for the gradient. In the process of proving the results we improve some of the gradient estimates obtained for the infinity harmonic functions. The lack of suitable gradient estimates has been a major obstacle for solving the C 1 , α problem in this setting, and we aim to take a step towards better understanding of this problem, too. A key tool in our approach is to study the problem in a suitable intrinsic geometry induced by the coefficient matrix A. Heuristically, this corresponds to considering the question on a Riemannian manifold whose the metric is given by the matrix A.

      PubDate: 2017-01-13T07:15:50Z
      DOI: 10.1016/j.anihpc.2015.10.003
       
  • L2-contraction for shock waves of scalar viscous conservation laws
    • Authors: Moon-Jin Kang; Alexis F. Vasseur
      Pages: 139 - 156
      Abstract: Publication date: January–February 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 1
      Author(s): Moon-Jin Kang, Alexis F. Vasseur
      We consider the L 2 -contraction up to a shift for viscous shocks of scalar viscous conservation laws with strictly convex fluxes in one space dimension. In the case of a flux which is a small perturbation of the quadratic Burgers flux, we show that any viscous shock induces a contraction in L 2 , up to a shift. That is, the L 2 norm of the difference of any solution of the viscous conservation law, with an appropriate shift of the shock wave, does not increase in time. If, in addition, the difference between the initial value of the solution and the shock wave is also bounded in L 1 , the L 2 norm of the difference converges at the optimal rate t − 1 / 4 . Both results do not involve any smallness condition on the initial value, nor on the size of the shock. In this context of small perturbations of the quadratic Burgers flux, the result improves the Choi and Vasseur's result in [7]. However, we show that the L 2 -contraction up to a shift does not hold for every convex flux. We construct a smooth strictly convex flux, for which the L 2 -contraction does not hold any more even along any Lipschitz shift.

      PubDate: 2017-01-13T07:15:50Z
      DOI: 10.1016/j.anihpc.2015.10.004
       
  • Asymptotic stability of solitary waves in generalized Gross–Neveu
           model
    • Authors: Andrew Comech; Tuoc Van Phan; Atanas Stefanov
      Pages: 157 - 196
      Abstract: Publication date: January–February 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 1
      Author(s): Andrew Comech, Tuoc Van Phan, Atanas Stefanov
      For the nonlinear Dirac equation in ( 1 + 1 ) D with scalar self-interaction (Gross–Neveu model), with quintic and higher order nonlinearities (and within certain range of the parameters), we prove that solitary wave solutions are asymptotically stable in the “even” subspace of perturbations (to ignore translations and eigenvalues ± 2 ω i ). The asymptotic stability is proved for initial data in H 1 . The approach is based on the spectral information about the linearization at solitary waves which we justify by numerical simulations. For the proof, we develop the spectral theory for the linearized operators and obtain appropriate estimates in mixed Lebesgue spaces, with and without weights.

      PubDate: 2017-01-13T07:15:50Z
      DOI: 10.1016/j.anihpc.2015.11.001
       
  • Finite time blowup for the parabolic–parabolic Keller–Segel system
           with critical diffusion
    • Authors: Philippe Laurençot; Noriko Mizoguchi
      Pages: 197 - 220
      Abstract: Publication date: January–February 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 1
      Author(s): Philippe Laurençot, Noriko Mizoguchi
      The present paper is concerned with the parabolic–parabolic Keller–Segel system ∂ t u = div ( ∇ u q + 1 − u ∇ v ) , t > 0 , x ∈ Ω , ∂ t v = Δ v − α v + u , t > 0 , x ∈ Ω , ( u , v ) ( 0 ) = ( u 0 , v 0 ) ≥ 0 , x ∈ Ω , with degenerate critical diffusion q = q ⋆ : = ( N − 2 ) / N in space dimension N ≥ 3 , the underlying domain Ω being either Ω = R N or the open ball Ω = B R ( 0 ) of R N with suitable boundary conditions. It has remained open whether there exist solutions blowing up in finite time, the existence of such solutions being known for the parabolic–elliptic reduction with the second equation replaced by 0 = Δ v − α v + u . Assuming that N = 3 , 4 and α > 0 , we prove that radially symmetric solutions with negative initial energy blow up in finite time in Ω = R N and in Ω = B R ( 0 ) under mixed Neumann–Dirichlet boundary conditions. Moreover, if Ω = B R ( 0 ) and Neumann boundary conditions are imposed on both u and v, we show the existence of a positive constant C depending only on N, Ω, and the mass of u 0 such that radially symmetric solutions blow up in finite time if the initial energy does not exceed −C. The criterion for finite time blowup is satisfied by a large class of initial data.

      PubDate: 2017-01-13T07:15:50Z
      DOI: 10.1016/j.anihpc.2015.11.002
       
  • Existence of a minimal non-scattering solution to the mass-subcritical
           generalized Korteweg–de Vries equation
    • Authors: Satoshi Masaki; Jun-ichi Segata
      Abstract: Publication date: Available online 20 April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Satoshi Masaki, Jun-ichi Segata
      In this article, we prove the existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical generalized Korteweg–de Vries (gKdV) equation in the scale critical L ˆ r space where L ˆ r = { f ∈ S ′ ( R ) ‖ f ‖ L ˆ r = ‖ f ˆ ‖ L r ′ < ∞ } . We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to L ˆ r -framework and approximation of solutions to the gKdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schrödinger equation.

      PubDate: 2017-04-25T17:12:45Z
      DOI: 10.1016/j.anihpc.2017.04.003
       
  • Long-Time Behavior of Solutions to the Derivative Nonlinear Schrödinger
           Equation for Soliton-Free Initial Data
    • Authors: Jiaqi Liu; Peter A. Perry; Catherine Sulem
      Abstract: Publication date: Available online 20 April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Jiaqi Liu, Peter A. Perry, Catherine Sulem
      The large-time behavior of solutions to the derivative nonlinear Schrödinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our approach uses the inverse scattering setting and the nonlinear steepest descent method of Deift and Zhou as recast by Dieng and McLaughlin.

      PubDate: 2017-04-25T17:12:45Z
      DOI: 10.1016/j.anihpc.2017.04.002
       
  • Ground states of pseudo-relativistic boson stars under the critical
           stellar mass
    • Authors: Yujin Guo; Xiaoyu Zeng
      Abstract: Publication date: Available online 19 April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Yujin Guo, Xiaoyu Zeng
      We consider ground states of pseudo-relativistic boson stars with a self-interacting potential K ( x ) in R 3 , which can be described by minimizers of the pseudo-relativistic Hartree energy functional. Under some assumptions on K ( x ) , minimizers exist if the stellar mass N satisfies 0 < N < N ⁎ , and there is no minimizer if N > N ⁎ , where N ⁎ is called the critical stellar mass. In contrast to the case of the Coulomb-type potential where K ( x ) ≡ 1 , we prove that the existence of minimizers may occur at N = N ⁎ , depending on the local profile of K ( x ) near the origin. When there is no minimizer at N = N ⁎ , we also present a detailed analysis of the behavior of minimizers as N approaches N ⁎ from below, for which the stellar mass concentrates at a unique point.

      PubDate: 2017-04-25T17:12:45Z
      DOI: 10.1016/j.anihpc.2017.04.001
       
  • Ancient shrinking spherical interfaces in the Allen–Cahn flow
    • Authors: Manuel del Pino; Konstantinos T. Gkikas
      Abstract: Publication date: Available online 4 April 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Manuel del Pino, Konstantinos T. Gkikas
      We consider the parabolic Allen–Cahn equation in R n , n ≥ 2 , u t = Δ u + ( 1 − u 2 ) u  in  R n × ( − ∞ , 0 ] . We construct an ancient radially symmetric solution u ( x , t ) with any given number k of transition layers between −1 and +1. At main order they consist of k time-traveling copies of w with spherical interfaces distant O ( log ⁡ t ) one to each other as t → − ∞ . These interfaces are resemble at main order copies of the shrinking sphere ancient solution to mean the flow by mean curvature of surfaces: x = − 2 ( n − 1 ) t . More precisely, if w ( s ) denotes the heteroclinic 1-dimensional solution of w ″ + ( 1 − w 2 ) w = 0 w ( ± ∞ ) = ± 1 given by w ( s ) = tanh ⁡ ( s 2 ) we have u ( x , t ) ≈ ∑ j = 1 k ( − 1 ) j − 1 w ( x − ρ j ( t ) ) − 1 2 ( 1 + ( − 1 ) k )  as  t → − ∞ where ρ j ( t ) = − 2 ( n − 1 ) t + 1 2 ( j − k + 1 2 ) log ⁡ ( t log ⁡ t ) + O (
      PubDate: 2017-04-11T15:39:24Z
      DOI: 10.1016/j.anihpc.2017.03.005
       
  • Analysis of miscible displacement through porous media with vanishing
           molecular diffusion and singular wells
    • Authors: Jérôme Droniou; Kyle S. Talbot
      Abstract: Publication date: Available online 30 March 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Jérôme Droniou, Kyle S. Talbot
      This article proves the existence of solutions to a model of incompressible miscible displacement through a porous medium, with zero molecular diffusion and modelling wells by spatial measures. We obtain the solution by passing to the limit on problems indexed by vanishing molecular diffusion coefficients. The proof employs cutoff functions to excise the supports of the measures and the discontinuities in the permeability tensor, thus enabling compensated compactness arguments used by Y. Amirat and A. Ziani for the analysis of the problem with L 2 wells (Amirat and Ziani, 2004 [1]). We give a novel treatment of the diffusion–dispersion term, which requires delicate use of the Aubin–Simon lemma to ensure the strong convergence of the pressure gradient, owing to the troublesome lower-order terms introduced by the localisation procedure.

      PubDate: 2017-04-03T14:57:29Z
      DOI: 10.1016/j.anihpc.2017.02.002
       
  • On the wellposedness of the KdV/KdV2 equations and their frequency maps
    • Authors: Thomas Kappeler; Jan-Cornelius Molnar
      Abstract: Publication date: Available online 28 March 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Thomas Kappeler, Jan-Cornelius Molnar
      In form of a case study for the KdV and the KdV2 equations, we present a novel approach of representing the frequencies of integrable PDEs which allows to extend them analytically to spaces of low regularity and to study their asymptotics. Applications include convexity properties of the Hamiltonians and wellposedness results in spaces of low regularity. In particular, it is proved that on H s the KdV2 equation is C 0 -wellposed if s ⩾ 0 and illposed (in a strong sense) if s < 0 .

      PubDate: 2017-04-03T14:57:29Z
      DOI: 10.1016/j.anihpc.2017.03.003
       
  • 3-D axisymmetric subsonic flows with nonzero swirl for the compressible
           Euler-Poisson system
    • Authors: Myoungjean Bae; Shangkun Weng
      Abstract: Publication date: Available online 28 March 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Myoungjean Bae, Shangkun Weng
      We address the structural stability of 3-D axisymmetric subsonic flows with nonzero swirl for the steady compressible Euler-Poisson system in a cylinder supplemented with non small boundary data. A special Helmholtz decomposition of the velocity field is introduced for 3-D axisymmetric flow with a nonzero swirl(=angular momentum density) component. With the newly introduced decomposition, a quasilinear elliptic system of second order is derived from the elliptic modes in Euler-Poisson system for subsonic flows. Due to the nonzero swirl, the main difficulties lie in the solvability of a singular elliptic equation which concerns the angular component of the vorticity in its cylindrical representation, and in analysis of streamlines near the axis r = 0 .

      PubDate: 2017-04-03T14:57:29Z
      DOI: 10.1016/j.anihpc.2017.03.004
       
  • Analysis of the loss of boundary conditions for the diffusive
           Hamilton-Jacobi equation
    • Authors: Alessio Porretta; Philippe Souplet
      Abstract: Publication date: Available online 21 March 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Alessio Porretta, Philippe Souplet
      We consider the diffusive Hamilton-Jacobi equation, with superquadratic Hamiltonian, homogeneous Dirichlet conditions and regular initial data. It is known from [4] (Barles-DaLio, 2004) that the problem admits a unique, continuous, global viscosity solution, which extends the classical solution in case gradient blowup occurs. We study the question of the possible loss of boundary conditions after gradient blowup, which seems to have remained an open problem till now. Our results show that the issue strongly depends on the initial data and reveal a rather rich variety of phenomena. For any smooth bounded domain, we construct initial data such that the loss of boundary conditions occurs everywhere on the boundary, as well as initial data for which no loss of boundary conditions occurs in spite of gradient blowup. Actually, we show that the latter possibility is rather exceptional. More generally, we show that the set of the points where boundary conditions are lost, can be prescribed to be arbitrarily close to any given open subset of the boundary.

      PubDate: 2017-03-27T14:30:31Z
      DOI: 10.1016/j.anihpc.2017.02.001
       
  • Quasistatic crack growth in 2d-linearized elasticity
    • Authors: Manuel Friedrich; Francesco Solombrino
      Abstract: Publication date: Available online 21 March 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Manuel Friedrich, Francesco Solombrino
      In this paper we prove a two-dimensional existence result for a variational model of crack growth for brittle materials in the realm of linearized elasticity. Starting with a time-discretized version of the evolution driven by a prescribed boundary load, we derive a time-continuous quasistatic crack growth in the framework of generalized special functions of bounded deformation ( G S B D ). As the time-discretization step tends to zero, the major difficulty lies in showing the stability of the static equilibrium condition, which is achieved by means of a Jump Transfer Lemma generalizing the result of [19] to the G S B D setting. Moreover, we present a general compactness theorem for this framework and prove existence of the evolution without imposing a-priori bounds on the displacements or applied body forces.

      PubDate: 2017-03-27T14:30:31Z
      DOI: 10.1016/j.anihpc.2017.03.002
       
  • On Lipschitz solutions for some forward–backward parabolic equations
    • Authors: Seonghak Kim; Baisheng Yan
      Abstract: Publication date: Available online 18 March 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Seonghak Kim, Baisheng Yan
      We investigate the existence and properties of Lipschitz solutions for some forward-backward parabolic equations in all dimensions. Our main approach to existence is motivated by reformulating such equations into partial differential inclusions and relies on a Baire's category method. In this way, the existence of infinitely many Lipschitz solutions to certain initial-boundary value problem of those equations is guaranteed under a pivotal density condition. Under this framework, we study two important cases of forward-backward anisotropic diffusion in which the density condition can be realized and therefore the existence results follow together with micro-oscillatory behavior of solutions. The first case is a generalization of the Perona-Malik model in image processing and the other that of Höllig's model related to the Clausius-Duhem inequality in the second law of thermodynamics.

      PubDate: 2017-03-20T13:19:06Z
      DOI: 10.1016/j.anihpc.2017.03.001
       
  • Plates with incompatible prestrain of high order
    • Authors: Marta Lewicka; Annie Raoult; Diego Ricciotti
      Abstract: Publication date: Available online 15 February 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Marta Lewicka, Annie Raoult, Diego Ricciotti
      We study the elastic behaviour of incompatibly prestrained thin plates of thickness h whose internal energy E h is governed by an imposed three-dimensional smooth Riemann metric G only depending on the variable in the midsurface ω. It is already known that h − 2 inf ⁡ E h converges to a finite value c when the metric G restricted to the midsurface has a sufficiently regular immersion, namely W 2 , 2 ( ω , R 3 ) . The obtained limit model generalizes the bending (Kirhchoff) model of Euclidean elasticity. In the present paper, we deal with the case when c equals 0. Then, equivalently, three independent entries of the three-dimensional Riemann curvature tensor associated with G are null. We prove that, in such regime, necessarily inf ⁡ E h ≤ C h 4 . We identify the Γ-limit of the scaled energies h − 4 E h and show that it consists of a von Kármán-like energy. The unknowns in this energy are the first order incremental displacements with respect to the deformation defined by the bending model and the second order tangential strains. In addition, we prove that when inf ⁡ h − 4 E h → 0 , then G is realizable and hence min ⁡ E h = 0 for every h.

      PubDate: 2017-02-17T03:27:12Z
      DOI: 10.1016/j.anihpc.2017.01.003
       
  • A global weak solution of the Dirac-harmonic map flow
    • Authors: Jürgen Jost; Lei Liu; Miaomiao Zhu
      Abstract: Publication date: Available online 11 February 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Jürgen Jost, Lei Liu, Miaomiao Zhu
      We show the existence of a global weak solution of the heat flow for Dirac-harmonic maps from compact Riemann surfaces with boundary when the energy of the initial map and the L 2 -norm of the boundary values of the spinor are sufficiently small. Dirac-harmonic maps couple a second order harmonic map type system with a first-order Dirac type system. The heat flow that has been introduced in [9] and that we investigate here is novel insofar as we only make the second order part parabolic, but carry the first order part along the resulting flow as an elliptic constraint. Of course, since the equations are coupled, both parts then change along the flow. The solution is unique and regular with the exception of at most finitely many singular times. We also discuss the behavior at the singularities of the flow. As an application, we deduce some existence results for Dirac-harmonic maps. Since we may impose nontrivial boundary conditions also for the spinor part, in the limit, we shall obtain Dirac-harmonic maps with nontrivial spinor part.

      PubDate: 2017-02-17T03:27:12Z
      DOI: 10.1016/j.anihpc.2017.01.002
       
  • A sharp Cauchy theory for the 2D gravity-capillary waves
    • Authors: Huy Quang Nguyen
      Abstract: Publication date: Available online 30 January 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Huy Quang Nguyen
      This article is devoted to the Cauchy problem for the 2D gravity-capillary water waves in fluid domains with general bottoms. Local well-posedness for this problem with Lipschitz initial velocity was established by Alazard–Burq–Zuily [1]. We prove that the Cauchy problem in Sobolev spaces is uniquely solvable for initial data 1 4 -derivative less regular than the aforementioned threshold, which corresponds to the gain of Hölder regularity of the semi-classical Strichartz estimate for the fully nonlinear system. In order to obtain this Cauchy theory, we establish global, quantitative results for the paracomposition theory of Alinhac [5].

      PubDate: 2017-02-04T11:27:21Z
      DOI: 10.1016/j.anihpc.2016.12.007
       
  • A quantitative theory for the continuity equation
    • Authors: Christian Seis
      Abstract: Publication date: Available online 27 January 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Christian Seis
      In this work, we provide stability estimates for the continuity equation with Sobolev vector fields. The results are inferred from contraction estimates for certain logarithmic Kantorovich–Rubinstein distances. As a by-product, we obtain a new proof of uniqueness in the DiPerna–Lions setting. The novelty in the proof lies in the fact that it is not based on the theory of renormalized solutions.

      PubDate: 2017-02-04T11:27:21Z
      DOI: 10.1016/j.anihpc.2017.01.001
       
  • The Kato smoothing effect for regularized Schrödinger equations in
           exterior domains
    • Authors: Lassaad Aloui; Moez Khenissi; Luc Robbiano
      Abstract: Publication date: Available online 27 January 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Lassaad Aloui, Moez Khenissi, Luc Robbiano
      We prove, under the exterior geometric control condition, the Kato smoothing effect for solutions of an inhomogeneous and damped Schrödinger equation on exterior domains.

      PubDate: 2017-02-04T11:27:21Z
      DOI: 10.1016/j.anihpc.2016.12.006
       
  • Damping of particles interacting with a vibrating medium
    • Authors: Ricardo Alonso; Thierry Goudon; Arthur Vavasseur
      Abstract: Publication date: Available online 9 January 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
      Author(s): Ricardo Alonso, Thierry Goudon, Arthur Vavasseur
      We investigate the large time behavior of the solutions of a Vlasov–Fokker–Planck equation where particles are subjected to a confining external potential and a self-consistent potential intended to describe the interaction of the particles with their environment. The environment is seen as a medium vibrating in a direction transverse to particles' motion. We identify equilibrium states of the model and justify the asymptotic trend to equilibrium. The analysis relies on hypocoercivity techniques.

      PubDate: 2017-01-13T07:15:50Z
      DOI: 10.1016/j.anihpc.2016.12.005
       
  • The Cauchy problem on large time for the Water Waves equations with large
           topography variations
    • Abstract: Publication date: January–February 2017
      Source:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 34, Issue 1
      Author(s): Benoît Mésognon-Gireau
      This paper shows that the long time existence of solutions to the Water Waves equations remains true with a large topography in presence of surface tension. More precisely, the dimensionless equations depend strongly on three parameters ε , μ , β measuring the amplitude of the waves, the shallowness and the amplitude of the bathymetric variations respectively. In [2], the local existence of solutions to this problem is proved on a time interval of size 1 max ⁡ ( β , ε ) and uniformly with respect to μ. In presence of large bathymetric variations (typically β ≫ ε ), the existence time is therefore considerably reduced. We remove here this restriction and prove the local existence on a time interval of size 1 ε under the constraint that the surface tension parameter must be at the same order as the shallowness parameter μ. We also show that the result of [5] dealing with large bathymetric variations for the Shallow Water equations can be viewed as a particular endpoint case of our result.

      PubDate: 2017-01-13T07:15:50Z
       
 
 
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