Evolution PDEs with Nonstandard Growth Conditions

Evolution PDEs with Nonstandard Growth Conditions

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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.A. Rodriguez, J. L. Vazquez, and J. R. Esteban, The maximal solution of the logarithmic fast diffusion equation in two space ... S. P. Kurdyumov, and A. P. Mikhailov, Blow-up in quasilinear parabolic equations, Walter de Gruyter aamp; Co., Berlin, 1995. ... Compact sets in the space L p(0, T; B), Ann. Mat. ... J. Simsen, A global attractor for a p(x)-Laplacian parabolic problem, Nonlinear Anal., 73 (2010 ), pp. ... S. L. Sobolev, Some applications of functional analysis in mathematical physics, vol.

Title:Evolution PDEs with Nonstandard Growth Conditions
Author: Stanislav Antontsev, Sergey Shmarev
Publisher:Springer - 2015-04-01

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