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    - APPLIED MATHEMATICS (81 journals)
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MATHEMATICS (723 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 32)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 4)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 14)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Science     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Nonlinear Analysis     Hybrid Journal  
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 12)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 6)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 9)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 2)
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 12)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 13)
Annals of Pure and Applied Logic     Open Access   (Followers: 3)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 13)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 9)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 21)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 12)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 19)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 8)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 30)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Econometrics     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)

        1 2 3 4 | Last

Journal Cover
Applied Mathematics & Optimization
Journal Prestige (SJR): 0.886
Citation Impact (citeScore): 1
Number of Followers: 9  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1432-0606 - ISSN (Online) 0095-4616
Published by Springer-Verlag Homepage  [2351 journals]
  • Exponential Asymptotic Stability for the Klein Gordon Equation on
           Non-compact Riemannian Manifolds
    • Authors: C. A. Bortot; M. M. Cavalcanti; V. N. Domingos Cavalcanti; P. Piccione
      Pages: 219 - 265
      Abstract: The Klein Gordon equation subject to a nonlinear and locally distributed damping, posed in a complete and non compact n dimensional Riemannian manifold \((\mathcal {M}^n,\mathbf {g})\) without boundary is considered. Let us assume that the dissipative effects are effective in \((\mathcal {M}\backslash \Omega ) \cup (\Omega \backslash V)\) , where \(\Omega \) is an arbitrary open bounded set with smooth boundary. In the present article we introduce a new class of non compact Riemannian manifolds, namely, manifolds which admit a smooth function f, such that the Hessian of f satisfies the pinching conditions (locally in \(\Omega \) ), for those ones, there exist a finite number of disjoint open subsets \( V_k\) free of dissipative effects such that \(\bigcup _k V_k \subset V\) and for all \(\varepsilon >0\) , \(meas(V)\ge meas(\Omega )-\varepsilon \) , or, in other words, the dissipative effect inside \(\Omega \) possesses measure arbitrarily small. It is important to be mentioned that if the function f satisfies the pinching conditions everywhere, then it is not necessary to consider dissipative effects inside \(\Omega \) .
      PubDate: 2018-10-01
      DOI: 10.1007/s00245-017-9405-5
      Issue No: Vol. 78, No. 2 (2018)
  • Local Exact Controllability of Two-Phase Field Solidification Systems with
           Few Controls
    • Authors: F. D. Araruna; B. M. R. Calsavara; E. Fernández-Cara
      Pages: 267 - 296
      Abstract: We analyze a control problem for a phase field system modeling the solidification process of materials that allow two different types of crystallization coupled to a Navier–Stokes system and a nonlinear heat equation, with a reduced number of controls. We prove that this system is locally exactly controllable to suitable trajectories, with controls acting only on the motion and heat equations.
      PubDate: 2018-10-01
      DOI: 10.1007/s00245-017-9406-4
      Issue No: Vol. 78, No. 2 (2018)
  • Optimal Control of a Degenerate PDE for Surface Shape
    • Authors: Harbir Antil; Shawn W. Walker
      Pages: 297 - 328
      Abstract: Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape in this paper. Specifically, we consider an objective (tracking) functional for surface shape with the prescribed mean curvature equation in graph form as a state constraint. The control variable is the prescribed curvature. We prove existence of an optimal control, and using improved regularity estimates, we show sufficient differentiability to make sense of the first order optimality conditions. This allows us to rigorously compute the gradient of the objective functional for both the continuous and discrete (finite element) formulations of the problem. Numerical results are shown to illustrate the minimizers and optimal controls on different domains.
      PubDate: 2018-10-01
      DOI: 10.1007/s00245-017-9407-3
      Issue No: Vol. 78, No. 2 (2018)
  • On a Dual Formulation for Growing Sandpile Problem with Mixed Boundary
    • Authors: N. Igbida; F. Karami; S. Ouaro; U. Traoré
      Pages: 329 - 359
      Abstract: In this work, we introduce and study a Prigozhin model for growing sandpile with mixed boundary conditions. For theoretical analysis we use semi-group theory and the numerical part is based on a duality approach.
      PubDate: 2018-10-01
      DOI: 10.1007/s00245-017-9408-2
      Issue No: Vol. 78, No. 2 (2018)
  • Stochastic Nonlinear Parabolic Equations with Stratonovich Gradient Noise
    • Authors: Viorel Barbu; Zdzisław Brzeźniak; Luciano Tubaro
      Pages: 361 - 377
      Abstract: Existence and uniqueness of solutions to stochastic differential equation \(dX-\text {div}\,a(\nabla X)\,dt=\sum _{j=1}^N(b_j\cdot \nabla X)\circ d\beta _j\) in \((0,T)\times \mathcal O\) ; \(X(0,\xi )=x(\xi )\) , \(\xi \in \mathcal O\) , \(X=0\) on \((0,T)\times \partial \mathcal O\) is studied. Here \(\mathcal O\) is a bounded and open domain of \(\mathbb R^d\) , \(d\ge 1\) , \(\{b_j\}\) is a divergence free vector field, \(a:[0,T]\times \mathcal O\times \mathbb R^d\rightarrow \mathbb R^d\) is a continuous and monotone mapping of subgradient type and \(\{\beta _j\}\) are independent Brownian motions in a probability space \((\Omega ,\mathcal F,\mathbb P)\) . The weak solution is defined via stochastic optimal control problem.
      PubDate: 2018-10-01
      DOI: 10.1007/s00245-017-9409-1
      Issue No: Vol. 78, No. 2 (2018)
  • Boundary Optimal Control for a Frictional Contact Problem with Normal
    • Authors: Andaluzia Matei; Sorin Micu
      Pages: 379 - 401
      Abstract: We consider the contact between an elastic body and a deformable foundation. Firstly, we introduce a mathematical model for this phenomenon by means of a normal compliance contact condition associated with a friction law. Then, we propose a variational formulation of the model in a form of a quasi-variational inequality governed by a non-differentiable functional and we briefly discuss its well-possedness. Nextly, we address an optimal control problem related to this model in order to led the displacement field as close as possible to a given target by acting with a localized boundary control. By using some mollifiers of the normal compliance functions, we introduce a regularized model which allows us to establish an optimality condition. Finally, by means of asymptotic analysis tools, we show that the solutions of the regularized optimal control problems converge to a solution of the initial optimal control problem.
      PubDate: 2018-10-01
      DOI: 10.1007/s00245-017-9410-8
      Issue No: Vol. 78, No. 2 (2018)
  • On the Existence, Uniqueness and Regularity of Solutions of a Viscoelastic
           Stokes Problem Modelling Salt Rocks
    • Authors: R. A. Cipolatti; I.-S. Liu; L. A. Palermo; M. A. Rincon; R. M. S. Rosa
      Pages: 403 - 456
      Abstract: A Stokes-type problem for a viscoelastic model of salt rocks is considered, and existence, uniqueness and regularity are investigated in the scale of \(L^2\) -based Sobolev spaces. The system is transformed into a generalized Stokes problem, and the proper conditions on the parameters of the model that guarantee that the system is uniformly elliptic are given. Under those conditions, existence, uniqueness and low-order regularity are obtained under classical regularity conditions on the data, while higher-order regularity is proved under less stringent conditions than classical ones. Explicit estimates for the solution in terms of the data are given accordingly.
      PubDate: 2018-10-01
      DOI: 10.1007/s00245-017-9411-7
      Issue No: Vol. 78, No. 2 (2018)
  • Critical Yield Numbers and Limiting Yield Surfaces of Particle Arrays
           Settling in a Bingham Fluid
    • Authors: José A. Iglesias; Gwenael Mercier; Otmar Scherzer
      Abstract: We consider the flow of multiple particles in a Bingham fluid in an anti-plane shear flow configuration. The limiting situation in which the internal and applied forces balance and the fluid and particles stop flowing, that is, when the flow settles, is formulated as finding the optimal ratio between the total variation functional and a linear functional. The minimal value for this quotient is referred to as the critical yield number or, in analogy to Rayleigh quotients, generalized eigenvalue. This minimum value can in general only be attained by discontinuous, hence not physical, velocities. However, we prove that these generalized eigenfunctions, whose jumps we refer to as limiting yield surfaces, appear as rescaled limits of the physical velocities. Then, we show the existence of geometrically simple minimizers. Furthermore, a numerical method for the minimization is then considered. It is based on a nonlinear finite difference discretization, whose consistency is proven, and a standard primal-dual descent scheme. Finally, numerical examples show a variety of geometric solutions exhibiting the properties discussed in the theoretical sections.
      PubDate: 2018-10-10
      DOI: 10.1007/s00245-018-9531-8
  • Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of
           Affine Systems
    • Authors: V. M. Veliov; P. T. Vuong
      Abstract: The paper presents new results about convergence of the gradient projection and the conditional gradient methods for abstract minimization problems on strongly convex sets. In particular, linear convergence is proved, although the objective functional does not need to be convex. Such problems arise, in particular, when a recently developed discretization technique is applied to optimal control problems which are affine with respect to the control. This discretization technique has the advantage to provide higher accuracy of discretization (compared with the known discretization schemes) and involves strongly convex constraints and possibly non-convex objective functional. The applicability of the abstract results is proved in the case of linear-quadratic affine optimal control problems. A numerical example is given, confirming the theoretical findings.
      PubDate: 2018-10-06
      DOI: 10.1007/s00245-018-9528-3
  • Linear Quadratic Optimal Control Problems with Fixed Terminal States and
           Integral Quadratic Constraints
    • Authors: Jingrui Sun
      Abstract: This paper is concerned with a linear quadratic (LQ, for short) optimal control problem with fixed terminal states and integral quadratic constraints. A Riccati equation with infinite terminal value is introduced, which is uniquely solvable and whose solution can be approximated by the solution for a suitable unconstrained LQ problem with penalized terminal state. Using results from duality theory, the optimal control is explicitly derived by solving the Riccati equation together with an optimal parameter selection problem. It turns out that the optimal control is a target-dependent feedback of the current state. Some examples are presented to illustrate the theory developed.
      PubDate: 2018-10-04
      DOI: 10.1007/s00245-018-9532-7
  • Approximate Controllability from the Exterior of Space-Time Fractional
           Wave Equations
    • Authors: Carole Louis-Rose; Mahamadi Warma
      Abstract: We investigate the controllability from the exterior of space-time fractional wave equations involving the Caputo time fractional derivative with the fractional Laplace operator subject to nonhomogeneous Dirichlet or Robin type exterior conditions. We prove that if \(1<\alpha < 2\) , \(0<s<1\) and \(\Omega \subset {{\mathbb {R}}}^N\) is a bounded Lipschitz domain, then the system $$\begin{aligned} {\left\{ \begin{array}{ll} {\mathbb {D}}_t^\alpha u+(-\Delta )^su=0\;\;&{} \text{ in } \;\;\Omega \times (0,T), \\ Bu=g\;&{} \text{ in } \; ({\mathbb {R}}^N\setminus \Omega )\times (0,T), \\ u(\cdot ,0)=u_0, \;\;\partial _tu(\cdot ,0)=u_1\;&{} \text{ in } \;\Omega , \end{array}\right. } \end{aligned}$$ is approximately controllable for any \(T>0\) , \((u_0,u_1)\in L^2(\Omega )\times {\mathbb {V}}_B^{-\frac{1}{\alpha }}\) and every \(g\in {\mathcal {D}}({\mathcal {O}}\times (0,T))\) , where \({\mathcal {O}}\subset ({\mathbb {R}}^N\setminus \Omega )\) is any non-empty open set in the case of the Dirichlet exterior condition \(Bu=u\) , and \({\mathcal {O}}\subseteq {\mathbb {R}}^N\setminus \Omega \) is any open set dense in \({\mathbb {R}}^N\setminus \Omega \) for the Robin exterior conditions \(Bu:=\mathcal N_su+\kappa u\) . Here, \({\mathcal {N}}_su\) is the nonlocal normal derivative of u and \({\mathbb {V}}_B^{-\frac{1}{\alpha }}\) denotes the dual of the domain of the fractional power of order \(\frac{1}{\alpha }\) of the realization in \(L^2(\Omega )\) of the operator \((-\Delta )^s\) with the zero (Dirichlet or Robin) exterior conditions \(Bu=0\) in \({{\mathbb {R}}}^N\setminus \Omega \) .
      PubDate: 2018-09-26
      DOI: 10.1007/s00245-018-9530-9
  • Optimal Control of a Vlasov–Poisson Plasma by Fixed Magnetic Field
    • Authors: Patrik Knopf; Jörg Weber
      Abstract: We consider the Vlasov–Poisson system that is equipped with an external magnetic field to describe the time evolution of the distribution function of a plasma. An optimal control problem where the external magnetic field is the control itself has already been investigated by Knopf (Calc Var 57:134, 2018). However, in real technical applications it will not be possible to choose the control field in such a general fashion as it will be induced by fixed field coils. In this paper we will use the fundamentals that were established by Knopf (Calc Var 57:134, 2018) to analyze an optimal control problem where the magnetic field is a superposition of the fields that are generated by N fixed magnetic field coils. Thereby, the aim is to control the plasma in such a way that its distribution function matches a desired distribution function at some certain final time T as closely as possible. This problem will be analyzed with respect to the following topics: existence of a globally optimal solution, necessary conditions of first order for local optimality, derivation of an optimality system, sufficient conditions of second order for local optimality and uniqueness of the optimal control under certain conditions.
      PubDate: 2018-09-25
      DOI: 10.1007/s00245-018-9526-5
  • Optimal Control and Zero-Sum Stochastic Differential Game Problems of
           Mean-Field Type
    • Authors: Boualem Djehiche; Said Hamadène
      Abstract: We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by weak solutions of stochastic differential equations of mean-field type.
      PubDate: 2018-09-25
      DOI: 10.1007/s00245-018-9525-6
  • Zero-Sum Stochastic Differential Game in Finite Horizon Involving Impulse
    • Authors: Brahim El Asri; Sehail Mazid
      Abstract: This paper considers the problem of two-player zero-sum stochastic differential game with both players adopting impulse controls in finite horizon under rather weak assumptions on the cost functions (c and \(\chi \) not decreasing in time). We use the dynamic programming principle and viscosity solutions approach to show existence and uniqueness of a solution for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) partial differential equation (PDE) of the game. We prove that the upper and lower value functions coincide.
      PubDate: 2018-09-24
      DOI: 10.1007/s00245-018-9529-2
  • Optimal Distributed Control of Two-Dimensional Nonlocal
           Cahn–Hilliard–Navier–Stokes Systems with Degenerate Mobility and
           Singular Potential
    • Authors: Sergio Frigeri; Maurizio Grasselli; Jürgen Sprekels
      Abstract: In this paper, we consider a two-dimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the Navier–Stokes equations, nonlinearly coupled with a convective nonlocal Cahn–Hilliard equation. The system rules the evolution of the (volume-averaged) velocity \(\varvec{u}\) of the mixture and the (relative) concentration difference \(\varphi \) of the two phases. The aim of this work is to study an optimal control problem for such a system, the control being a time-dependent external force \(\varvec{v}\) acting on the fluid. We first prove the existence of an optimal control for a given tracking type cost functional. Then we study the differentiability properties of the control-to-state map \(\varvec{v}\mapsto [\varvec{u},\varphi ]\) , and we establish first-order necessary optimality conditions. These results generalize the ones obtained by the first and the third authors jointly with Rocca (SIAM J Control Optim 54:221–250, 2016). There the authors assumed a constant mobility and a regular potential with polynomially controlled growth. Here, we analyze the physically more relevant case of a degenerate mobility and a singular (e.g., logarithmic) potential. This is made possible by the existence of a unique strong solution which was recently proved by the authors and Gal (WIAS preprint series No. 2309, Berlin, 2016).
      PubDate: 2018-09-24
      DOI: 10.1007/s00245-018-9524-7
  • On Cross-Diffusion Systems for Two Populations Subject to a Common
           Congestion Effect
    • Authors: Maxime Laborde
      Abstract: In this paper, we investigate the existence of solution for systems of Fokker–Planck equations coupled through a common nonlinear congestion. Two different kinds of congestion are considered: a porous media congestion or soft congestion and the hard congestion given by the constraint \(\rho _1+\rho _2 \leqslant 1\) . We show that these systems can be seen as gradient flows in a Wasserstein product space and then we obtain a constructive method to prove the existence of solutions. Therefore it is natural to apply it for numerical purposes and some numerical simulations are included.
      PubDate: 2018-09-22
      DOI: 10.1007/s00245-018-9527-4
  • Correction to: Remarks on Hierarchic Control for a Linearized Micropolar
           Fluids System in Moving Domains
    • Authors: Isaías Pereira de Jesus
      Abstract: The original version of this article unfortunately contained a mistake in the equation.
      PubDate: 2018-09-18
      DOI: 10.1007/s00245-018-9522-9
  • Mean–Variance Asset–Liability Management Problem Under Non-Markovian
           Regime-Switching Models
    • Authors: Yang Shen; Jiaqin Wei; Qian Zhao
      Abstract: In this paper, we study an asset–liability management problem under a mean–variance criterion with regime switching. Unlike previous works, the dynamics of assets and liability are described by non-Markovian regime-switching models in the sense that all the model parameters are predictable with respect to the filtration generated jointly by a Markov chain and a Brownian motion. The problem is solved with the aid of backward stochastic differential equations (BSDEs) and bounded mean oscillation martingales. An efficient strategy and an efficient frontier are obtained and represented by unique solutions to several relevant BSDEs. We show that the optimal capital structure can be achieved when the initial asset value is expressed by a linear combination of the initial liability and the expected surplus. It is further found that a mutual fund theorem holds not only for the efficient strategy, but also for the optimal capital structure.
      PubDate: 2018-09-11
      DOI: 10.1007/s00245-018-9523-8
  • Nonlinear, Nonhomogeneous Robin Problems with Indefinite Potential and
           General Reaction
    • Authors: Nikolaos S. Papageorgiou; Vicenţiu D. Rădulescu; Dušan D. Repovš
      Abstract: We consider a nonlinear elliptic equation driven by a nonhomogeneous differential operator plus an indefinite potential. On the reaction term we impose conditions only near zero. Using variational methods, together with truncation and perturbation techniques and critical groups, we produce three nontrivial solutions with sign information. In the semilinear case we improve this result by obtaining a second nodal solution for a total of four nontrivial solutions. Finally, under a symmetry condition on the reaction term, we generate a whole sequence of distinct nodal solutions.
      PubDate: 2018-09-07
      DOI: 10.1007/s00245-018-9521-x
  • Rank Theorem in Infinite Dimension and Lagrange Multipliers
    • Authors: Joël Blot
      Abstract: We use an extension to the infinite dimension of the rank theorem of the differential calculus to establish a Lagrange theorem for optimization problems in Banach spaces. We provide an application to variational problems on a space of bounded sequences under equality constraints.
      PubDate: 2018-09-05
      DOI: 10.1007/s00245-018-9520-y
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