EXISTENCE RESULT FOR NONLINEAR PARABOLIC EQUATIONS WITH LOWER ORDER TERMS

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 vertical bar u vertical bar(gamma-1)u) + b vertical bar del u vertical bar(delta) = f - divg 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 is an element of (L-r(Q(T)))(N) with r = N+p/p-1, delta = N(p-1)+p/N+2, b is an element of L-N+2,L-1(Q(T)), f is an element of L-1(Q(T)), g is an element of (Lp' (Q(T)))(N) and u(0) is an element of L-1(Omega).