ENGLISH

Evolution PDEs with Nonstandard Growth Conditions: Existence, Uniqueness, Localization, Blow-up

By Stanislav Antontsev , Sergey Shmarev (auth.)

Book information

Publisher
Atlantis Press
Year
2015
ISBN
978-94-6239-111-6, 978-94-6239-112-3
DOI
10.2991/978-94-6239-112-3
Language
english
Format
PDF
Filesize
4 MB (4281504 bytes)
Series
Atlantis Studies in Differential Equations 4
Edition
1
Pages
409\417
Time added
2015-04-23 16:00:00
Partial Differential Equations; Functional Analysi

Description

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.

Similar books