Nonlinear parabolic problem with lower order terms in Musielak-Orlicz spaces

Abstract

We prove an existence result of entropy solutions for the nonlinear parabolic problems:∂b (x,u) ∂t u, ∇u)) is a Leary-Lions operator defined on the inhomogeneous Musielak-Orlicz space, the term Φ(x, t, u) is a Crathéodory function assumed to be continuous on u and satisfy only the growth con-