Parabolic inequalities in inhomogeneous Orlicz-Sobolev spaces with gradients constraints and L¹-data

This work is devoted to the study of a new class of parabolic problems in inhomogeneous Orlicz spaces with gradient constraints and L¹-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 L¹-data involving the parameter p.