Existence and extinction of solutions for parabolic equations with nonstandard growth nonlinearity.

Abstract

In this paper, we consider an initial boundary value problem for a class of p(⋅)-Laplacian parabolic equation with nonstandard nonlinearity in a bounded domain. We obtain the global and decay of existence of the solutions for small initial data and for some suitable conditions on the parameter λ. Moreover, the precise decay estimates of solutions before the occurrence of the extinction are derived.