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

• Main Authors: Antontsev, Stanislav (Author), Shmarev, Sergey (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Paris : Atlantis Press : Imprint: Atlantis Press, 2015.
• Series: Atlantis Studies in Differential Equations, 4
• Subjects: Mathematics.; Functional analysis.; Partial differential equations.; Partial Differential Equations.; Functional Analysis.

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...

Table of Contents:

• 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.