Evolution PDEs with nonstandard growth conditions [electronic resource] : existence, uniqueness, localization, blow-up / Stanislav Antontsev, Sergey Shmarev.
Antont͡sev, S. N. (Stanislav Nikolaevich), author.; Shmarev, S. I., author.
2015
QA377
Available Online

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Title Evolution PDEs with nonstandard growth conditions [electronic resource] : existence, uniqueness, localization, blow-up / Stanislav Antontsev, Sergey Shmarev.
Author Antont͡sev, S. N. (Stanislav Nikolaevich), author.
ISBN 9789462391123 electronic book
9462391122 electronic book
9789462391116
DOI https://doi.org/10.2991/978-94-6239-112-3
Published Paris : Atlantis Press, 2015.
Language English
Description 1 online resource.
Item Number 10.2991/978-94-6239-112-3 doi
Call Number QA377
Dewey Decimal Classification 515.353
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (viewed April 8, 2015).
Added Author Shmarev, S. I., author.
Series Atlantis studies in differential equations ; v. 4.
Available in Other Form Print version: 9789462391116
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The function spaces
A porous medium equation with variable nonlinearity
Localization of solutions of the generalized Porous Medium Equation
Anisotropic equations with variable growth and coercivity conditions
Space localization of energy solutions
Extinction in a finite time and the large time behavior
Blow-up in equations with variable nonlinearity
Equations with double isotropic nonlinearity
Strong solutions of doubly nonlinear anisotropic equations
Anisotropic equations with double nonlinearity: blow-up and vanishing
Wave equation with p(x, t )-Laplacian
Semilinear hyperbolic equations.

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