SOME INITIAL-OBLIQUE DERIVATIVE BOUNDARY VALUE PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS WITH UNBOUNDED COEFFICIENTS

In this paper, we consider quasilinear uniformly parabolic equations: Lu = aij (t, x, u)Diju b(t, x u, Du) - ut = 0, with regular derivative boundary value problems: Bu = u/ v au = h(t, x). By the help of Leray-schauder fixed point theorem, we get the a priori estimates and the existence theorem.