ON PARABOLIC INITIAL-BOUNDARY VALUE-PROBLEMS WITH CRITICAL GROWTH FORTHE GRADIENT

We prove the existence of weak solutions for the initial-boundary valu e problem of the quasilinear parabolic equation partial derivative u/p artial derivative t + A(u) + g(x, t, u, Du) = f Here A is a Leray-Lion s type operator from V = L(P) (0, T; W-0(1), W-0(p) (OMEGA)) to its du al space V, g is a nonlinear term with critical growth with respect t o Du satisfying a sign condition and no growth condition with respect to u; f is a given element in V.