Evolution PDEs with Nonstandard Growth Conditions
Existence, Uniqueness, Localization, Blow-up
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Beschreibung
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.
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.
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 Includes supplementary material: sn.pub/extras
Autor*in
Stanislav Antontsev
Themen in »Evolution PDEs with Nonstandard Growth Conditions«
Blow-up Localization of solutions in space and time Nonlinear parabolic and hyperbolic equations Nonstandard growth conditions Variable and anisotropic nonlinearity partial differential equations