On The Third Initial Boundary Value Problems Of Parabolic HESSIAN Equations

In 1995,Ivochkina and Ladyzhenskaya discussed the first initial-boundary value problems of the followed two forms equations,they obtained the existence and uniqueness of the classical solutions in [5] and [6].where (D2u) - (A1,..., An) is the eigenvalue of the Hessian matrix of the unknown function u(x. t] (for the fixed t). If k=n,the equation (2) is the equation (1).In 1998.Wang Guanglie and Liu Huizhao [7] generalized the equation of [6].they studied the first initial-boundary value problems of the equationHere / satisfied the conditions used in [3], Caffarelli,Nirenberg and Spruck studied thecorresponding elliptic differential equations. Specially, f = S satisfied the all additive conditions of / in [3].In 2000,Zhou Wenshu gained the existence and uniqueness of the strict convex classical solutions of the third initial-boundary value problems of the Monge - Ampere. equation in [10].The purpose of this paper is to extend the result on the above parabolic equations to the case of genetic equationBy employing proper auxiliary functions and barrier functions in the case of unchanging the conditions of [10],we obtained the priori estimations.So we gained the existence and uniqueness of the strict convex classical solution by utilizing the continuous method.