Existence and Uniqueness of Entropy Solution For Nonlinear Periodic Parabolic Problem with Orlicz growth and L1 Data

Abstract

In this paper we prove the existence and uniqueness of entropy solution for a nonlinear periodic parabolic problem in the setting of Orlicz spaces represented by the following equation :

                                                      ∂u/∂t + A(u) = f (x, t).
Where A is a Leray-Lions operator defined on a subset of

W^{1,x}_{0} L_{M}](QT) and f belongs to L^{1}(Q_T).