Evolution PDEs with Nonstandard Growth Conditions
Existence, Uniqueness, Localization, Blow-up
Authors: Antontsev, Stanislav, Shmarev, Sergey
Free Preview- The first systematic exposition of the theory of evolution PDEs with nonstandard growth conditions
- Specific tools for the study of PDEs with nonstandard growth are developed
- New localization effects due to anisotropy and variable nonlinearity are discovered
- A number of new not previously published results is included
- A review of other approaches and known results is provided
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- About this book
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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.
- Table of contents (12 chapters)
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The Function Spaces
Pages 1-43
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A Porous Medium Equation with Variable Nonlinearity
Pages 45-80
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Localization of Solutions of the Generalized Porous Medium Equation
Pages 81-105
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Anisotropic Equations with Variable Growth and Coercivity Conditions
Pages 107-184
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Space Localization of Energy Solutions
Pages 185-217
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Table of contents (12 chapters)
- Download Preface 1 PDF (93.9 KB)
- Download Sample pages 2 PDF (339.2 KB)
- Download Table of contents PDF (198 KB)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Evolution PDEs with Nonstandard Growth Conditions
- Book Subtitle
- Existence, Uniqueness, Localization, Blow-up
- Authors
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- Stanislav Antontsev
- Sergey Shmarev
- Series Title
- Atlantis Studies in Differential Equations
- Series Volume
- 4
- Copyright
- 2015
- Publisher
- Atlantis Press
- Copyright Holder
- Atlantis Press and the author(s)
- eBook ISBN
- 978-94-6239-112-3
- DOI
- 10.2991/978-94-6239-112-3
- Hardcover ISBN
- 978-94-6239-111-6
- Series ISSN
- 2214-6253
- Edition Number
- 1
- Number of Pages
- XVII, 409
- Number of Illustrations
- 1 b/w illustrations
- Topics
