NONLINEAR PARABOLIC EQUATIONS WITH A LOWER ORDER TERM AND L1 DATA

In this paper we prove the existence of a renormalized solution for a class of nonlinear parabolic problems whose prototype is. {partial derivative u/partial derivative t - Delta(p)u + div(c(x,t)|u|(gamma-1) u) = f in Q(T) u(x,t) = 0 on partial derivative Omega x (0,T) u(x, 0) = u(0)(x) in Omega, where Q(T) = Omega x (0, T), Omega is an open and bounded subset of R-N, N >= 2, T > 0, Delta(p) is the so called p-Laplace operator, gamma = (N + 2)(p - 1)/N+p, c(x,t) is an element of(L-tau(Q(T)))N, tau= N+p/p-1, f is an element of L-1(Q(T)), u(0) is an element of L-1(Omega).