Evolution PDEs with nonstandard growth conditions [Documento electrónico] : existence, uniqueness, localization, blow-up / Stanislav Antontsev, Sergey Shmarev
Language: eng.Country: US - United States of America.Publication: Paris : Atlantis Press, Atlantis Press, 2015Description: XVII, 409 p. : il.ISBN: 978-94-6239-112-3.Series: Atlantis Studies in Differential EquationsSubject - Topical Name: 3647 | 4913Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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QA374.SPR FCT 96539 Applied partial differential equations | QA374.SPR FCT 96587 Solutions of nonlinear Schrӧdinger systems | QA374.SPR FCT 96654 An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞ | QA374.SPR FCT 96714 Evolution PDEs with nonstandard growth conditions, existence, uniqueness, localization, blow-up | QA374.SPR FCT 96734 From particle systems to partial differential equations II, particle systems and PDEs II, Braga, Portugal, December 2013 | QA374.SPR FCT 96804 Elliptic–hyperbolic partial differential equations, a mini-course in geometric and quasilinear methods | QA374.SPR FCT 96808 Differential geometry and continuum mechanics |
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This monograph offers the reader a treatment of the theory of evolution PDEs with nonstandard growth conditions. This class includes parabolic and hyperbolic equations with variable or anisotropic nonlinear structure. We develop methods for the study of such equations and present a detailed account of recent results. An overview of other approaches to the study of PDEs of this kind is provided. The presentation is focused on the issues of existence and uniqueness of solutions in appropriate function spaces, and on the study of the specific qualitative properties of solutions, such as localization in space and time, extinction in a finite time and blow-up, or nonexistence of global in time solutions. Special attention is paid to the study of the properties intrinsic to solutions of equations with nonstandard growth.
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