Strongly nonlinear parabolic equations with natural growth terms in Orlicz spaces

摘要

We prove approximation and compactness results in inhomogeneous Orlicz-Sobolev spaces and look at, as an application, the Cauchy-Dirichlet equation u' + A(u) + g(x, t, u, delU) = f is an element of W--1,W- x E-M, where A is a Leray-Lions operator having a growth not necessarily of polynomial type. We also give a trace result allowing to deduce the continuity of the solutions with respect to time. (C) 2004 Elsevier Ltd. All rights reserved.