Titlebook: Evolution PDEs with Nonstandard Growth Conditions; Existence, Uniquenes Stanislav Antontsev,Sergey Shmarev Book 2015 The Editor(s) (if appl

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A Porous Medium Equation with Variable Nonlinearity,We devote this chapter to study the homogeneous Dirichlet problem for the semilinear parabolic equation which generalizes the Porous Medium Equation.

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Space Localization of Energy Solutions,This chapter is devoted to study the properties of finite speed of propagation and space localization of solutions of parabolic PDEs with nonstandard growth.

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Extinction in a Finite Time and the Large Time Behavior,This chapter continues the study of the propagation properties of solutions of the Dirichlet problem for the anisotropic parabolic equations with variable nonlinearity. We study the large time behavior and the possibility of extinction of solutions in a finite time.

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Blow-up in Equations with Variable Nonlinearity,A remarkable property of nonlinear evolution equations is the possibility of formation of singularities in solutions of problems with smooth input data, which leads to blow-up, or explosion, of initially regular solutions.

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Equations with Double Isotropic Nonlinearity,In this chapter we study the Dirichlet problem for the class of equations with double variable nonlinearity

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Anisotropic Equations with Double Nonlinearity: Blow-up and Vanishing,This chapter is devoted to the study of qualitative properties of strong solutions of the Dirichlet problem for the doubly nonlinear anisotropic parabolic equation with variable nonlinearity

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