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Publisher: Springer-Verlag (Total: 2352 journals)

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Showing 1 - 200 of 2352 Journals sorted alphabetically
3D Printing in Medicine     Open Access   (Followers: 2)
3D Research     Hybrid Journal   (Followers: 21, SJR: 0.222, CiteScore: 1)
4OR: A Quarterly J. of Operations Research     Hybrid Journal   (Followers: 10, SJR: 0.825, CiteScore: 1)
AAPS J.     Hybrid Journal   (Followers: 23, SJR: 1.118, CiteScore: 4)
AAPS PharmSciTech     Hybrid Journal   (Followers: 7, SJR: 0.752, CiteScore: 3)
Abdominal Imaging     Hybrid Journal   (Followers: 17, SJR: 0.866, CiteScore: 2)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4, SJR: 0.439, CiteScore: 0)
Academic Psychiatry     Full-text available via subscription   (Followers: 27, SJR: 0.53, CiteScore: 1)
Academic Questions     Hybrid Journal   (Followers: 8, SJR: 0.106, CiteScore: 0)
Accreditation and Quality Assurance: J. for Quality, Comparability and Reliability in Chemical Measurement     Hybrid Journal   (Followers: 29, SJR: 0.316, CiteScore: 1)
Acoustical Physics     Hybrid Journal   (Followers: 11, SJR: 0.359, CiteScore: 1)
Acoustics Australia     Hybrid Journal   (SJR: 0.232, CiteScore: 1)
Acta Analytica     Hybrid Journal   (Followers: 7, SJR: 0.367, CiteScore: 0)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1, SJR: 0.675, CiteScore: 1)
Acta Biotheoretica     Hybrid Journal   (Followers: 4, SJR: 0.284, CiteScore: 1)
Acta Diabetologica     Hybrid Journal   (Followers: 19, SJR: 1.587, CiteScore: 3)
Acta Endoscopica     Hybrid Journal   (Followers: 1)
acta ethologica     Hybrid Journal   (Followers: 4, SJR: 0.769, CiteScore: 1)
Acta Geochimica     Hybrid Journal   (Followers: 7, SJR: 0.24, CiteScore: 1)
Acta Geodaetica et Geophysica     Hybrid Journal   (Followers: 3, SJR: 0.305, CiteScore: 1)
Acta Geophysica     Hybrid Journal   (Followers: 11, SJR: 0.312, CiteScore: 1)
Acta Geotechnica     Hybrid Journal   (Followers: 7, SJR: 1.588, CiteScore: 3)
Acta Informatica     Hybrid Journal   (Followers: 5, SJR: 0.517, CiteScore: 1)
Acta Mathematica     Hybrid Journal   (Followers: 13, SJR: 7.066, CiteScore: 3)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2, SJR: 0.452, CiteScore: 1)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6, SJR: 0.379, CiteScore: 1)
Acta Mathematica Vietnamica     Hybrid Journal   (SJR: 0.27, CiteScore: 0)
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal   (SJR: 0.208, CiteScore: 0)
Acta Mechanica     Hybrid Journal   (Followers: 21, SJR: 1.04, CiteScore: 2)
Acta Mechanica Sinica     Hybrid Journal   (Followers: 5, SJR: 0.607, CiteScore: 2)
Acta Metallurgica Sinica (English Letters)     Hybrid Journal   (Followers: 7, SJR: 0.576, CiteScore: 2)
Acta Meteorologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.638, CiteScore: 1)
Acta Neurochirurgica     Hybrid Journal   (Followers: 7, SJR: 0.822, CiteScore: 2)
Acta Neurologica Belgica     Hybrid Journal   (Followers: 1, SJR: 0.376, CiteScore: 1)
Acta Neuropathologica     Hybrid Journal   (Followers: 4, SJR: 7.589, CiteScore: 12)
Acta Oceanologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.334, CiteScore: 1)
Acta Physiologiae Plantarum     Hybrid Journal   (Followers: 3, SJR: 0.574, CiteScore: 2)
Acta Politica     Hybrid Journal   (Followers: 15, SJR: 0.605, CiteScore: 1)
Activitas Nervosa Superior     Hybrid Journal   (SJR: 0.147, CiteScore: 0)
adhäsion KLEBEN & DICHTEN     Hybrid Journal   (Followers: 8, SJR: 0.103, CiteScore: 0)
ADHD Attention Deficit and Hyperactivity Disorders     Hybrid Journal   (Followers: 25, SJR: 0.72, CiteScore: 2)
Adhesion Adhesives & Sealants     Hybrid Journal   (Followers: 9)
Administration and Policy in Mental Health and Mental Health Services Research     Partially Free   (Followers: 17, SJR: 1.005, CiteScore: 2)
Adsorption     Hybrid Journal   (Followers: 5, SJR: 0.703, CiteScore: 2)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4, SJR: 0.698, CiteScore: 1)
Advances in Atmospheric Sciences     Hybrid Journal   (Followers: 37, SJR: 0.956, CiteScore: 2)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 19, SJR: 0.812, CiteScore: 1)
Advances in Contraception     Hybrid Journal   (Followers: 3)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 59, SJR: 1.09, CiteScore: 1)
Advances in Gerontology     Partially Free   (Followers: 8, SJR: 0.144, CiteScore: 0)
Advances in Health Sciences Education     Hybrid Journal   (Followers: 30, SJR: 1.64, CiteScore: 2)
Advances in Manufacturing     Hybrid Journal   (Followers: 4, SJR: 0.475, CiteScore: 2)
Advances in Polymer Science     Hybrid Journal   (Followers: 45, SJR: 1.04, CiteScore: 3)
Advances in Therapy     Hybrid Journal   (Followers: 5, SJR: 1.075, CiteScore: 3)
Aegean Review of the Law of the Sea and Maritime Law     Hybrid Journal   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2, SJR: 0.517, CiteScore: 1)
Aerobiologia     Hybrid Journal   (Followers: 3, SJR: 0.673, CiteScore: 2)
Aesthetic Plastic Surgery     Hybrid Journal   (Followers: 11, SJR: 0.825, CiteScore: 1)
African Archaeological Review     Hybrid Journal   (Followers: 21, SJR: 0.862, CiteScore: 1)
Afrika Matematika     Hybrid Journal   (Followers: 1, SJR: 0.235, CiteScore: 0)
AGE     Hybrid Journal   (Followers: 7)
Ageing Intl.     Hybrid Journal   (Followers: 7, SJR: 0.39, CiteScore: 1)
Aggiornamenti CIO     Hybrid Journal   (Followers: 1)
Aging Clinical and Experimental Research     Hybrid Journal   (Followers: 3, SJR: 0.67, CiteScore: 2)
Agricultural Research     Hybrid Journal   (Followers: 6, SJR: 0.276, CiteScore: 1)
Agriculture and Human Values     Hybrid Journal   (Followers: 14, SJR: 1.173, CiteScore: 3)
Agroforestry Systems     Hybrid Journal   (Followers: 20, SJR: 0.663, CiteScore: 1)
Agronomy for Sustainable Development     Hybrid Journal   (Followers: 13, SJR: 1.864, CiteScore: 6)
AI & Society     Hybrid Journal   (Followers: 9, SJR: 0.227, CiteScore: 1)
AIDS and Behavior     Hybrid Journal   (Followers: 14, SJR: 1.792, CiteScore: 3)
Air Quality, Atmosphere & Health     Hybrid Journal   (Followers: 4, SJR: 0.862, CiteScore: 3)
Akupunktur & Aurikulomedizin     Full-text available via subscription   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 6, SJR: 0.531, CiteScore: 0)
Algebra Universalis     Hybrid Journal   (Followers: 2, SJR: 0.583, CiteScore: 1)
Algebras and Representation Theory     Hybrid Journal   (Followers: 1, SJR: 1.095, CiteScore: 1)
Algorithmica     Hybrid Journal   (Followers: 9, SJR: 0.56, CiteScore: 1)
Allergo J.     Full-text available via subscription   (Followers: 1, SJR: 0.234, CiteScore: 0)
Allergo J. Intl.     Hybrid Journal   (Followers: 2)
Alpine Botany     Hybrid Journal   (Followers: 5, SJR: 1.11, CiteScore: 3)
ALTEX : Alternatives to Animal Experimentation     Open Access   (Followers: 3)
AMBIO     Hybrid Journal   (Followers: 10, SJR: 1.569, CiteScore: 4)
American J. of Cardiovascular Drugs     Hybrid Journal   (Followers: 16, SJR: 0.951, CiteScore: 3)
American J. of Community Psychology     Hybrid Journal   (Followers: 29, SJR: 1.329, CiteScore: 2)
American J. of Criminal Justice     Hybrid Journal   (Followers: 9, SJR: 0.772, CiteScore: 1)
American J. of Cultural Sociology     Hybrid Journal   (Followers: 17, SJR: 0.46, CiteScore: 1)
American J. of Dance Therapy     Hybrid Journal   (Followers: 5, SJR: 0.181, CiteScore: 0)
American J. of Potato Research     Hybrid Journal   (Followers: 2, SJR: 0.611, CiteScore: 1)
American J. of Psychoanalysis     Hybrid Journal   (Followers: 21, SJR: 0.314, CiteScore: 0)
American Sociologist     Hybrid Journal   (Followers: 14, SJR: 0.35, CiteScore: 0)
Amino Acids     Hybrid Journal   (Followers: 8, SJR: 1.135, CiteScore: 3)
AMS Review     Partially Free   (Followers: 4)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 7, SJR: 0.211, CiteScore: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5, SJR: 0.536, CiteScore: 1)
Analysis in Theory and Applications     Hybrid Journal   (Followers: 1)
Analysis of Verbal Behavior     Hybrid Journal   (Followers: 6)
Analytical and Bioanalytical Chemistry     Hybrid Journal   (Followers: 32, SJR: 0.978, CiteScore: 3)
Anatomical Science Intl.     Hybrid Journal   (Followers: 3, SJR: 0.367, CiteScore: 1)
Angewandte Schmerztherapie und Palliativmedizin     Hybrid Journal  
Angiogenesis     Hybrid Journal   (Followers: 3, SJR: 2.177, CiteScore: 5)
Animal Cognition     Hybrid Journal   (Followers: 20, SJR: 1.389, CiteScore: 3)
Annales françaises de médecine d'urgence     Hybrid Journal   (Followers: 1, SJR: 0.192, CiteScore: 0)
Annales Henri Poincaré     Hybrid Journal   (Followers: 3, SJR: 1.097, CiteScore: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4, SJR: 0.438, CiteScore: 0)
Annali dell'Universita di Ferrara     Hybrid Journal   (SJR: 0.429, CiteScore: 0)
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1, SJR: 1.197, CiteScore: 1)
Annals of Biomedical Engineering     Hybrid Journal   (Followers: 17, SJR: 1.042, CiteScore: 3)
Annals of Combinatorics     Hybrid Journal   (Followers: 4, SJR: 0.932, CiteScore: 1)
Annals of Data Science     Hybrid Journal   (Followers: 12)
Annals of Dyslexia     Hybrid Journal   (Followers: 10, SJR: 0.85, CiteScore: 2)
Annals of Finance     Hybrid Journal   (Followers: 32, SJR: 0.579, CiteScore: 1)
Annals of Forest Science     Hybrid Journal   (Followers: 7, SJR: 0.986, CiteScore: 2)
Annals of Global Analysis and Geometry     Hybrid Journal   (Followers: 1, SJR: 1.228, CiteScore: 1)
Annals of Hematology     Hybrid Journal   (Followers: 15, SJR: 1.043, CiteScore: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12, SJR: 0.413, CiteScore: 1)
Annals of Microbiology     Hybrid Journal   (Followers: 11, SJR: 0.479, CiteScore: 2)
Annals of Nuclear Medicine     Hybrid Journal   (Followers: 5, SJR: 0.687, CiteScore: 2)
Annals of Operations Research     Hybrid Journal   (Followers: 10, SJR: 0.943, CiteScore: 2)
Annals of Ophthalmology     Hybrid Journal   (Followers: 12)
Annals of Regional Science     Hybrid Journal   (Followers: 8, SJR: 0.614, CiteScore: 1)
Annals of Software Engineering     Hybrid Journal   (Followers: 13)
Annals of Solid and Structural Mechanics     Hybrid Journal   (Followers: 9, SJR: 0.239, CiteScore: 1)
Annals of Surgical Oncology     Hybrid Journal   (Followers: 15, SJR: 1.986, CiteScore: 4)
Annals of Telecommunications     Hybrid Journal   (Followers: 9, SJR: 0.223, CiteScore: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1, SJR: 1.495, CiteScore: 1)
Antonie van Leeuwenhoek     Hybrid Journal   (Followers: 5, SJR: 0.834, CiteScore: 2)
Apidologie     Hybrid Journal   (Followers: 4, SJR: 1.22, CiteScore: 3)
APOPTOSIS     Hybrid Journal   (Followers: 9, SJR: 1.424, CiteScore: 4)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2, SJR: 0.294, CiteScore: 1)
Applications of Mathematics     Hybrid Journal   (Followers: 2, SJR: 0.602, CiteScore: 1)
Applied Biochemistry and Biotechnology     Hybrid Journal   (Followers: 44, SJR: 0.571, CiteScore: 2)
Applied Biochemistry and Microbiology     Hybrid Journal   (Followers: 18, SJR: 0.21, CiteScore: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 5, SJR: 0.49, CiteScore: 0)
Applied Composite Materials     Hybrid Journal   (Followers: 49, SJR: 0.58, CiteScore: 2)
Applied Entomology and Zoology     Partially Free   (Followers: 6, SJR: 0.422, CiteScore: 1)
Applied Geomatics     Hybrid Journal   (Followers: 3, SJR: 0.733, CiteScore: 3)
Applied Geophysics     Hybrid Journal   (Followers: 9, SJR: 0.488, CiteScore: 1)
Applied Intelligence     Hybrid Journal   (Followers: 13, SJR: 0.6, CiteScore: 2)
Applied Magnetic Resonance     Hybrid Journal   (Followers: 4, SJR: 0.319, CiteScore: 1)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 8, SJR: 0.886, CiteScore: 1)
Applied Mathematics - A J. of Chinese Universities     Hybrid Journal   (SJR: 0.17, CiteScore: 0)
Applied Mathematics and Mechanics     Hybrid Journal   (Followers: 5, SJR: 0.461, CiteScore: 1)
Applied Microbiology and Biotechnology     Hybrid Journal   (Followers: 66, SJR: 1.182, CiteScore: 4)
Applied Physics A     Hybrid Journal   (Followers: 10, SJR: 0.481, CiteScore: 2)
Applied Physics B: Lasers and Optics     Hybrid Journal   (Followers: 24, SJR: 0.74, CiteScore: 2)
Applied Psychophysiology and Biofeedback     Hybrid Journal   (Followers: 8, SJR: 0.519, CiteScore: 2)
Applied Research in Quality of Life     Hybrid Journal   (Followers: 12, SJR: 0.316, CiteScore: 1)
Applied Solar Energy     Hybrid Journal   (Followers: 22, SJR: 0.225, CiteScore: 0)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 7, SJR: 0.542, CiteScore: 1)
Aquaculture Intl.     Hybrid Journal   (Followers: 26, SJR: 0.591, CiteScore: 2)
Aquarium Sciences and Conservation     Hybrid Journal   (Followers: 2)
Aquatic Ecology     Hybrid Journal   (Followers: 36, SJR: 0.656, CiteScore: 2)
Aquatic Geochemistry     Hybrid Journal   (Followers: 4, SJR: 0.591, CiteScore: 1)
Aquatic Sciences     Hybrid Journal   (Followers: 13, SJR: 1.109, CiteScore: 3)
Arabian J. for Science and Engineering     Hybrid Journal   (Followers: 5, SJR: 0.303, CiteScore: 1)
Arabian J. of Geosciences     Hybrid Journal   (Followers: 2, SJR: 0.319, CiteScore: 1)
Archaeological and Anthropological Sciences     Hybrid Journal   (Followers: 21, SJR: 1.052, CiteScore: 2)
Archaeologies     Hybrid Journal   (Followers: 12, SJR: 0.224, CiteScore: 0)
Archiv der Mathematik     Hybrid Journal   (Followers: 1, SJR: 0.725, CiteScore: 1)
Archival Science     Hybrid Journal   (Followers: 65, SJR: 0.745, CiteScore: 2)
Archive for History of Exact Sciences     Hybrid Journal   (Followers: 7, SJR: 0.186, CiteScore: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3, SJR: 0.909, CiteScore: 1)
Archive for Rational Mechanics and Analysis     Hybrid Journal   (SJR: 3.93, CiteScore: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6, SJR: 0.79, CiteScore: 2)
Archives and Museum Informatics     Hybrid Journal   (Followers: 153, SJR: 0.101, CiteScore: 0)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6, SJR: 1.41, CiteScore: 5)
Archives of Dermatological Research     Hybrid Journal   (Followers: 7, SJR: 1.006, CiteScore: 2)
Archives of Environmental Contamination and Toxicology     Hybrid Journal   (Followers: 14, SJR: 0.773, CiteScore: 2)
Archives of Gynecology and Obstetrics     Hybrid Journal   (Followers: 17, SJR: 0.956, CiteScore: 2)
Archives of Microbiology     Hybrid Journal   (Followers: 9, SJR: 0.644, CiteScore: 2)
Archives of Orthopaedic and Trauma Surgery     Hybrid Journal   (Followers: 9, SJR: 1.146, CiteScore: 2)
Archives of Osteoporosis     Hybrid Journal   (Followers: 2, SJR: 0.71, CiteScore: 2)
Archives of Sexual Behavior     Hybrid Journal   (Followers: 10, SJR: 1.493, CiteScore: 3)
Archives of Toxicology     Hybrid Journal   (Followers: 17, SJR: 1.541, CiteScore: 5)
Archives of Virology     Hybrid Journal   (Followers: 5, SJR: 0.973, CiteScore: 2)
Archives of Women's Mental Health     Hybrid Journal   (Followers: 16, SJR: 1.274, CiteScore: 3)
Archivio di Ortopedia e Reumatologia     Hybrid Journal  
Archivum Immunologiae et Therapiae Experimentalis     Hybrid Journal   (Followers: 2, SJR: 0.946, CiteScore: 3)
ArgoSpine News & J.     Hybrid Journal  
Argumentation     Hybrid Journal   (Followers: 6, SJR: 0.349, CiteScore: 1)
Arid Ecosystems     Hybrid Journal   (Followers: 2, SJR: 0.2, CiteScore: 0)
Arkiv för Matematik     Hybrid Journal   (Followers: 2, SJR: 0.766, CiteScore: 1)
Arnold Mathematical J.     Hybrid Journal   (Followers: 1, SJR: 0.355, CiteScore: 0)
Arthropod-Plant Interactions     Hybrid Journal   (Followers: 2, SJR: 0.839, CiteScore: 2)
Arthroskopie     Hybrid Journal   (Followers: 1, SJR: 0.131, CiteScore: 0)
Artificial Intelligence and Law     Hybrid Journal   (Followers: 11, SJR: 0.937, CiteScore: 2)
Artificial Intelligence Review     Hybrid Journal   (Followers: 18, SJR: 0.833, CiteScore: 4)
Artificial Life and Robotics     Hybrid Journal   (Followers: 9, SJR: 0.226, CiteScore: 0)
Asia Europe J.     Hybrid Journal   (Followers: 5, SJR: 0.504, CiteScore: 1)
Asia Pacific Education Review     Hybrid Journal   (Followers: 12, SJR: 0.479, CiteScore: 1)
Asia Pacific J. of Management     Hybrid Journal   (Followers: 16, SJR: 1.185, CiteScore: 2)
Asia-Pacific Education Researcher     Hybrid Journal   (Followers: 13, SJR: 0.353, CiteScore: 1)
Asia-Pacific Financial Markets     Hybrid Journal   (Followers: 3, SJR: 0.187, CiteScore: 0)
Asia-Pacific J. of Atmospheric Sciences     Hybrid Journal   (Followers: 19, SJR: 0.855, CiteScore: 1)
Asian Business & Management     Hybrid Journal   (Followers: 9, SJR: 0.378, CiteScore: 1)
Asian J. of Business Ethics     Hybrid Journal   (Followers: 10)
Asian J. of Criminology     Hybrid Journal   (Followers: 6, SJR: 0.543, CiteScore: 1)
AStA Advances in Statistical Analysis     Hybrid Journal   (Followers: 5, SJR: 0.548, CiteScore: 1)
AStA Wirtschafts- und Sozialstatistisches Archiv     Hybrid Journal   (Followers: 5, SJR: 0.183, CiteScore: 0)
ästhetische dermatologie & kosmetologie     Full-text available via subscription  
Astronomy and Astrophysics Review     Hybrid Journal   (Followers: 22, SJR: 3.385, CiteScore: 5)

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Journal Cover
Archive for Rational Mechanics and Analysis
Journal Prestige (SJR): 3.93
Citation Impact (citeScore): 3
Number of Followers: 0  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1432-0673 - ISSN (Online) 0003-9527
Published by Springer-Verlag Homepage  [2352 journals]
  • Doubly Nonlinear Equations of Porous Medium Type
    • Authors: Verena Bögelein; Frank Duzaar; Paolo Marcellini; Christoph Scheven
      Pages: 503 - 545
      Abstract: In this paper we prove the existence of solutions to doubly nonlinear equations whose prototype is given by $$\partial_t u^m- {\rm div}\, D_{\xi}\, f(x,Du) =0,$$ with \({m\in (0,\infty )}\) , or more generally with an increasing and piecewise C1 nonlinearity b and a function f depending on u $$\partial_{t}b(u) - {\rm div}\, D_{\xi}\, f(x,u,Du)= -D_u f(x,u,Du).$$ For the function f we merely assume convexity and coercivity, so that, for instance, \({f(x,u,\xi)=\alpha(x) \xi ^p + \beta(x) \xi ^q}\) with 1 < p < q and non-negative coefficients α, β with \({\alpha(x)+\beta(x)\geqq \nu > 0}\) , and \({f(\xi)=\exp(\tfrac12 \xi ^2)}\) are covered. Thus, for functions \({f(x,u,\xi )}\) satisfying only a coercivity assumption from below but very general growth conditions from above, we prove the existence of variational solutions; mean while, if \({f(x,u,\xi )}\) grows naturally when \({\left\vert \xi \right\vert \rightarrow +\infty }\) as a polynomial of order p (for instance in the case of the p-Laplacian operator), then we obtain the existence of solutions in the sense of distributions as well as the existence of weak solutions. Our technique is purely variational and we treat both the cases of bounded and unbounded domains. We introduce a nonlinear version of the minimizing movement approach that could also be useful for the numerics of doubly nonlinear equations.
      PubDate: 2018-08-01
      DOI: 10.1007/s00205-018-1221-9
      Issue No: Vol. 229, No. 2 (2018)
  • On the Second Boundary Value Problem for Monge–Ampère Type
           Equations and Geometric Optics
    • Authors: Feida Jiang; Neil S. Trudinger
      Pages: 547 - 567
      Abstract: In this paper, we prove the existence of classical solutions to second boundary value problems for generated prescribed Jacobian equations, as recently developed by the second author, thereby obtaining extensions of classical solvability of optimal transportation problems to problems arising in near field geometric optics. Our results depend in particular on a priori second derivative estimates recently established by the authors under weak co-dimension one convexity hypotheses on the associated matrix functions with respect to the gradient variables, (A3w). We also avoid domain deformations by using the convexity theory of generating functions to construct unique initial solutions for our homotopy family, thereby enabling application of the degree theory for nonlinear oblique boundary value problems.
      PubDate: 2018-08-01
      DOI: 10.1007/s00205-018-1222-8
      Issue No: Vol. 229, No. 2 (2018)
  • Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems
    • Authors: Andrea Cianchi; Vladimir G. Maz’ya
      Pages: 569 - 599
      Abstract: Best possible second-order regularity is established for solutions to p-Laplacian type equations with \({p \in (1, \infty)}\) and a square-integrable right-hand side. Our results provide a nonlinear counterpart of the classical L2-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are obtained. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required, although our conclusions are new even for smooth domains. If the domain is convex, no regularity of its boundary is needed at all.
      PubDate: 2018-08-01
      DOI: 10.1007/s00205-018-1223-7
      Issue No: Vol. 229, No. 2 (2018)
  • Three-Scale Singular Limits of Evolutionary PDEs
    • Authors: Bin Cheng; Qiangchang Ju; Steve Schochet
      Pages: 601 - 625
      Abstract: Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly bounded for a fixed time as the two parameters tend to zero at different rates. A simple example shows the necessity of those conditions in order for uniform bounds to hold. Under further conditions the solutions of the original system tend to solutions of a limit equation as the parameters tend to zero.
      PubDate: 2018-08-01
      DOI: 10.1007/s00205-018-1233-5
      Issue No: Vol. 229, No. 2 (2018)
  • On the Boltzmann Equation with Stochastic Kinetic Transport: Global
           Existence of Renormalized Martingale Solutions
    • Authors: Samuel Punshon-Smith; Scott Smith
      Pages: 627 - 708
      Abstract: This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of renormalized (in the sense of DiPerna/Lions) martingale solutions to the Boltzmann equation for large initial data with finite mass, energy, and entropy. Our analysis includes a detailed study of weak martingale solutions to a class of linear stochastic kinetic equations. This study includes a criterion for renormalization, the weak closedness of the solution set, and tightness of velocity averages in \({{L}^{1}}\) .
      PubDate: 2018-08-01
      DOI: 10.1007/s00205-018-1225-5
      Issue No: Vol. 229, No. 2 (2018)
  • Boundary Equations and Regularity Theory for Geometric Variational Systems
           with Neumann Data
    • Authors: Armin Schikorra
      Pages: 709 - 788
      Abstract: We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, intersect perpendicularly with a support manifold. For example, harmonic maps, or H-surfaces, with a partially free boundary condition. In the interior it is known, by the celebrated work of Rivière, that these maps satisfy a system with an antisymmetric potential, from which one can derive the interior regularity of the solution. Avoiding a reflection argument, we show that these maps satisfy along the boundary a system of equations which also exhibits a (nonlocal) antisymmetric potential that combines information from the interior potential and the geometric Neumann boundary condition. We then proceed to show boundary regularity for solutions to such systems.
      PubDate: 2018-08-01
      DOI: 10.1007/s00205-018-1226-4
      Issue No: Vol. 229, No. 2 (2018)
  • A Conceptual Approach to the Problem of Action-Angle Variables
    • Authors: Nguyen Tien Zung
      Pages: 789 - 833
      Abstract: In this paper we develop a general conceptual approach to the problem of existence of action-angle variables for dynamical systems, which establishes and uses the fundamental conservation property of associated torus actions: anything which is preserved by the system is also preserved by the associated torus actions. This approach allows us to obtain, among other things: (a) the shortest and most easy-to-understand conceptual proof of the classical Arnold–Liouville–Mineur theorem; (b) basically all known results in the literature about the existence of action-angle variables in various contexts can be recovered in a unifying way, with simple proofs, using our approach; (c) new results on action-angle variables in many different contexts, including systems on contact manifolds, systems on presymplectic and Dirac manifolds, action-angle variables near singularities, stochastic systems, and so on. Even when there are no natural action variables, our approach still leads to useful normal forms for dynamical systems, which are not necessarily integrable.
      PubDate: 2018-08-01
      DOI: 10.1007/s00205-018-1227-3
      Issue No: Vol. 229, No. 2 (2018)
  • Time-Domain Analysis of an Acoustic–Elastic Interaction Problem
    • Authors: Gang Bao; Yixian Gao; Peijun Li
      Pages: 835 - 884
      Abstract: Consider the scattering of a time-domain acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous air or fluid. This paper concerns the mathematical analysis of such a time-domain acoustic–elastic interaction problem. An exact transparent boundary condition (TBC) is developed to reduce the scattering problem from an open domain into an initial-boundary value problem in a bounded domain. The well-posedness and stability are established for the reduced problem. A priori estimates with explicit time dependence are achieved for the pressure of the acoustic wave field and the displacement of the elastic wave field. Our proof is based on the method of energy, the Lax–Milgram lemma, and the inversion theorem of the Laplace transform. In addition, a time-domain absorbing perfectly matched layer (PML) method is introduced to replace the nonlocal TBC by a Dirichlet boundary condition. A first order symmetric hyperbolic system is derived for the truncated PML problem. The well-posedness and stability are proved. The time-domain PML results are expected to be useful in the computational air/fluid–solid interaction problems.
      PubDate: 2018-08-01
      DOI: 10.1007/s00205-018-1228-2
      Issue No: Vol. 229, No. 2 (2018)
  • The Propagation of Chaos for a Rarefied Gas of Hard Spheres in the Whole
    • Authors: Ryan Denlinger
      Pages: 885 - 952
      Abstract: We discuss old and new results on the mathematical justification of Boltzmann’s equation. The classical result along these lines is a theorem which was proven by Lanford in the 1970s. This paper is naturally divided into three parts. I. Classical. We give new proofs of both the uniform bounds required for Lanford’s theorem, as well as the related bounds due to Illner and Pulvirenti for a perturbation of vacuum. The proofs use a duality argument and differential inequalities, instead of a fixed point iteration. II. Strong chaos. We introduce a new notion of propagation of chaos. Our notion of chaos provides for uniform error estimates on a very precise set of points; this set is closely related to the notion of strong (one-sided) chaos and the emergence of irreversibility. III. Supplemental. We announce and provide a proof (in “Appendix A”) of the propagation of partial factorization at some phase-points where complete factorization is impossible.
      PubDate: 2018-08-01
      DOI: 10.1007/s00205-018-1229-1
      Issue No: Vol. 229, No. 2 (2018)
  • Relative Entropy for Hyperbolic–Parabolic Systems and Application to the
           Constitutive Theory of Thermoviscoelasticity
    • Authors: Cleopatra Christoforou; Athanasios E. Tzavaras
      Pages: 1 - 52
      Abstract: We extend the relative entropy identity to the class of hyperbolic–parabolic systems whose hyperbolic part is symmetrizable. The resulting identity, in the general theory, is useful for providing stability of viscous solutions and yields a convergence result in the zero-viscosity limit to smooth solutions in an L p framework. It also provides a weak–strong uniqueness theorem for measure valued solutions of the hyperbolic problem. In the second part, the relative entropy identity is developed for the systems of gas dynamics for viscous and heat conducting gases and for the system of thermoviscoelasticity both including viscosity and heat-conduction effects. The dissipation mechanisms and the concentration measures play different roles when applying the method to the general class of hyperbolic–parabolic systems and to the specific examples, and their ramifications are highlighted.
      PubDate: 2018-07-01
      DOI: 10.1007/s00205-017-1212-2
      Issue No: Vol. 229, No. 1 (2018)
  • Discretely Self-Similar Solutions to the Navier–Stokes Equations
           with Besov Space Data
    • Authors: Zachary Bradshaw; Tai-Peng Tsai
      Pages: 53 - 77
      Abstract: We construct self-similar solutions to the three dimensional Navier–Stokes equations for divergence free, self-similar initial data that can be large in the critical Besov space \({\dot{B}_{p,\infty}^{3/p-1}}\) where 3 < p < 6. We also construct discretely self-similar solutions for divergence free initial data in \({\dot{B}_{p,\infty}^{3/p-1}}\) for 3 < p < 6 that is discretely self-similar for some scaling factor λ > 1. These results extend those of Bradshaw and Tsai (Ann Henri Poincaré 2016. which dealt with initial data in L 3 w since \({L^3_w\subsetneq \dot{B}_{p,\infty}^{3/p-1}}\) for p > 3. We also provide several concrete examples of vector fields in the relevant function spaces.
      PubDate: 2018-07-01
      DOI: 10.1007/s00205-017-1213-1
      Issue No: Vol. 229, No. 1 (2018)
  • Data-Driven Problems in Elasticity
    • Authors: S. Conti; S. Müller; M. Ortiz
      Pages: 79 - 123
      Abstract: We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of approximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within this Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to material data sets that are not graphs.
      PubDate: 2018-07-01
      DOI: 10.1007/s00205-017-1214-0
      Issue No: Vol. 229, No. 1 (2018)
  • Defects in Nematic Shells: A Γ-Convergence Discrete-to-Continuum
    • Authors: Giacomo Canevari; Antonio Segatti
      Pages: 125 - 186
      Abstract: In this paper we rigorously investigate the emergence of defects on Nematic Shells with a genus different from one. This phenomenon is related to a non-trivial interplay between the topology of the shell and the alignment of the director field. To this end, we consider a discrete XY system on the shell M, described by a tangent vector field with unit norm sitting at the vertices of a triangulation of the shell. Defects emerge when we let the mesh size of the triangulation go to zero, namely in the discrete-to-continuum limit. In this paper we investigate the discrete-to-continuum limit in terms of Γ-convergence in two different asymptotic regimes. The first scaling promotes the appearance of a finite number of defects whose charges are in accordance with the topology of shell M, via the Poincaré–Hopf Theorem. The second scaling produces the so called Renormalized Energy that governs the equilibrium of the configurations with defects.
      PubDate: 2018-07-01
      DOI: 10.1007/s00205-017-1215-z
      Issue No: Vol. 229, No. 1 (2018)
  • Spatial Double Choreographies of the Newtonian 2 n -Body Problem
    • Authors: Guowei Yu
      Pages: 187 - 229
      Abstract: In this paper, for the spatial Newtonian 2n-body problem with equal masses, by proving that the minimizers of the action functional under certain symmetric, topological and monotone constraints are collision-free, we found a family of spatial double choreographies, which have the common feature that half of the masses are circling around the z-axis clockwise along a spatial loop, while the motions of the other half of the masses are given by a rotation of the first half around the x-axis by π. Both loops are simple, without any self-intersection, and symmetric with respect to the xz-plane and yz-plane. The set of intersection points between the two loops is non-empty and contained in the xy-plane. The number of such double choreographies grows exponentially as n goes to infinity.
      PubDate: 2018-07-01
      DOI: 10.1007/s00205-018-1216-6
      Issue No: Vol. 229, No. 1 (2018)
  • Multi-dimensional Wave Propagation Over a Burgers Shock Profile
    • Authors: Tai-Ping Liu; Shih-Hsien Yu
      Pages: 231 - 337
      Abstract: We study the stability of viscous shock profiles under multi-dimensional perturbation in order to understand the propagation ofmulti-dimensional dispersionwaves over the compressive shock profile. Our analysis is based on the new algorithm of explicitly constructing the Green’s function for the system linearized around the shock profile. We first construct Green’s function for the system linearized around the inviscid profile by matching the two half space problems. The Green’s function around the shock profile is then constructed by iterations. Our approach is of a general nature. We carry out the approach for a simple model possessing the Burgers shocks and wave structure similar to acoustic cones in multi-dimensional gas flows. The approach exhibits a rich phenomenon of wave propagation along and dispersing away from the shock profile.
      PubDate: 2018-07-01
      DOI: 10.1007/s00205-018-1217-5
      Issue No: Vol. 229, No. 1 (2018)
  • Global Regularity of 2D Density Patches for Inhomogeneous
    • Authors: Francisco Gancedo; Eduardo García-Juárez
      Pages: 339 - 360
      Abstract: This paper is about Lions’ open problem on density patches (Lions in Mathematical topics in fluid mechanics. Vol. 1, volume 3 of Oxford Lecture series in mathematics and its applications, Clarendon Press, Oxford University Press, New York, 1996): whether or not inhomogeneous incompressible Navier–Stokes equations preserve the initial regularity of the free boundary given by density patches. Using classical Sobolev spaces for the velocity, we first establish the propagation of \({C^{1+\gamma}}\) regularity with \({0 < \gamma < 1}\) in the case of positive density. Furthermore, we go beyond this to show the persistence of a geometrical quantity such as the curvature. In addition, we obtain a proof for \({C^{2+\gamma}}\) regularity.
      PubDate: 2018-07-01
      DOI: 10.1007/s00205-018-1218-4
      Issue No: Vol. 229, No. 1 (2018)
  • A Duality Theory for Non-convex Problems in the Calculus of Variations
    • Authors: Guy Bouchitté; Ilaria Fragalà
      Pages: 361 - 415
      Abstract: We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min–max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375–379, 2015).
      PubDate: 2018-07-01
      DOI: 10.1007/s00205-018-1219-3
      Issue No: Vol. 229, No. 1 (2018)
  • Sharp Interface Limit for a Stokes/Allen–Cahn System
    • Authors: Helmut Abels; Yuning Liu
      Pages: 417 - 502
      Abstract: We consider the sharp interface limit of a coupled Stokes/Allen–Cahn system, when a parameter \({\epsilon > 0}\) that is proportional to the thickness of the diffuse interface tends to zero, in a two dimensional bounded domain. For sufficiently small times we prove convergence of the solutions of the Stokes/Allen–Cahn system to solutions of a sharp interface model, where the interface evolution is given by the mean curvature equation with an additional convection term coupled to a two-phase Stokes system with an additional contribution to the stress tensor, which describes the capillary stress. To this end we construct a suitable approximation of the solution of the Stokes/Allen–Cahn system, using three levels of the terms in the formally matched asymptotic calculations, and estimate the difference with the aid of a suitable refinement of a spectral estimate of the linearized Allen–Cahn operator. Moreover, a careful treatment of the coupling terms is needed.
      PubDate: 2018-07-01
      DOI: 10.1007/s00205-018-1220-x
      Issue No: Vol. 229, No. 1 (2018)
  • Nonconvex Model of Material Growth: Mathematical Theory
    • Authors: J. F. Ganghoffer; P. I. Plotnikov; J. Sokolowski
      Abstract: The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.
      PubDate: 2018-06-02
      DOI: 10.1007/s00205-018-1259-8
  • Large Time Behavior of Solutions to 3-D MHD System with Initial Data Near
    • Authors: Wen Deng; Ping Zhang
      Abstract: Califano and Chiuderi (Phys Rev E 60 (PartB):4701–4707, 1999) conjectured that the energy of an incompressible Magnetic hydrodynamical system is dissipated at a rate that is independent of the ohmic resistivity. The goal of this paper is to mathematically justify this conjecture in three space dimensions provided that the initial magnetic field and velocity is a small perturbation of the equilibrium state (e3, 0). In particular, we prove that for such data, a 3-D incompressible MHD system without magnetic diffusion has a unique global solution. Furthermore, the velocity field and the difference between the magnetic field and e3 decay to zero in both L∞ and L2 norms with explicit rates. We point out that the decay rate in the L2 norm is optimal in sense that this rate coincides with that of the linear system. The main idea of the proof is to exploit Hörmander’s version of the Nash–Moser iteration scheme, which is very much motivated by the seminar papers by Klainerman (Commun Pure Appl Math 33:43–101, 1980, Arch Ration Mech Anal 78:73–98, 1982, Long time behaviour of solutions to nonlinear wave equations. PWN, Warsaw, pp 1209–1215, 1984) on the long time behavior to the evolution equations.
      PubDate: 2018-06-02
      DOI: 10.1007/s00205-018-1265-x
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