Parabolic inequalities in inhomogeneous Orlicz-Sobolev spaces with gradients constraints and L 1-data

Abstract

Abstract This work is devoted to the study of a new class of parabolic problems in inhomogeneous Orlicz spaces with gradient constraints and L 1-data. One proves the existence of the solution by studying the asymptotic behaviour as p goes to ∞, of a sequence of entropy solutions (up ) of some nonlinear parabolic equation in inhomogeneous Orlicz-Sobolev spaces with L 1-data involving the parameter p.