Abstract
This paper is concerned with the study of the nonlinear Dirichlet parabolic problem in a bounded subset Omega subset of IRN
u(t) + Au + g(x, t, u, del u) = f - div phi(u),
where A is an operator of Leray-Lions type acted from the parabolic anisotropic space L-(p) over right arrow(0, T; W-0(1, (p) over right arrow) (Omega)) into its dual. g is a nonlinear term having a growth condition with respect to del u and satisfying a sign condition with no growth condition with respect to u. In addition, when the initial condition u(0) and the data f are assumed to be merely integrable and phi(.) is an element of C-0(IR, IRN), we prove the existence of entropy solutions for this class of problems.