Evolution PDEs with Nonstandard Growth Conditions

Existence, Uniqueness, Localization, Blow-up

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Differential Equations
Cover of the book Evolution PDEs with Nonstandard Growth Conditions by Stanislav Antontsev, Sergey Shmarev, Atlantis Press
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Author: Stanislav Antontsev, Sergey Shmarev ISBN: 9789462391123
Publisher: Atlantis Press Publication: April 1, 2015
Imprint: Atlantis Press Language: English
Author: Stanislav Antontsev, Sergey Shmarev
ISBN: 9789462391123
Publisher: Atlantis Press
Publication: April 1, 2015
Imprint: Atlantis Press
Language: English

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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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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