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 ?nite 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.