Existence, Uniqueness and Blow-up Result of Solutions for an Evolution p(x)−laplacian Equation

Abstract

In this paper we are investigate in the evolution equation p(x)-laplacian with the initial boundary value question. We translate the parabolic equation into the elliptic equation by using a finite difference method, and then the existence and uniqueness solution are obtained. The blow-up property is shown, by using the energy method. We perform, using Matlab (Ode45 subroutine), some numerical experiments just to illustrate our general results.