THE BOUNDARY VALUE PROBLEMS FOR THE HIGHER ORDER QUASILINEAR PARABOLIC AND ELLIPTIC SYSTEMS SATISFYING GENERAL BOUNDARY CONDITIONS

In this paper, the existence and uniqueness of the boundary value problems for the higher order quasilinear parabolic systems satisfying general boundary conditions and initial value condition are considered. We have concluded the problems to the following: if all the solutions of a family of problems of the same type which are derived from a substitution of τf(s, t, u, ...,Dx2b-1u), τgj（y, t, u） and τ（x） （0≤τ≤1） for f, g, and φ respectively are uniformly bounded, then the original problems have a unique solution in H2b+a,1+a/2b（（?）T）. Under assumption that the linear problems have a unique solution, we have proved the existence and uniqueness of the solution of the boundary value problems for the quasillnear elliptic systems.