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

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 ( u p ) of some nonlinear parabolic equation in inhomogeneous Orlicz-Sobolev spaces with L 1 -data involving the parameter p .