Existence, Uniqueness and Blow-up Result of Solutions for an Evolution p(x)−laplacian Equation
Hamid El Ouardi *
Research laboratory in Engineering (LRI), University Hassan II of Casablanca, National Higher School of Electricity and Mechanics, Equipe S´ecurit ´ e, Syst`emes & Mod´ elisations. ENSEM, BP. 8118, Km7, Morocco.
*Author to whom correspondence should be addressed.
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.
Keywords: p(x)-laplacian equation, existence, uniqueness, numerical blow-up, variable exponents, difference method