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

摘要

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