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

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.