l'étude d'une équation hyperbolique non linéaire à exposants variables

Abstract

This work is devoted to the study of a nonlinear viscoelastic hyperbolic equation with variable exponents. We recall some basic notions of functional analysis, in particular Banach spaces and Sobolev spaces. Then, we introduce the spaces of Orlicz-Sobolev functions and give a brief description of their essential properties. Using Galerkin's method, we show the existence of weak solutions as well as their explosion, the latter being established under appropriate assumptions of sufficient conditions on m, p and initial data