Strongly nonlinear parabolic equations with natural growth terms in Orlicz spaces Original Research Article

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,∇u)=f∈W-1,xEMu′+A(u)+g(x,t,u,∇u)=f∈W-1,xEM, where AA 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.