Abstract:

We investigated the first initial boundary value problem of  -u_t+log S_k(λ(D²u))=ψ(x,t,u), which is a class of parabolic k-Hessian equations. In the general smooth region Ω, under the admissible subsolution, a prior estimation of the admissible solution was given. The existence of the admissible solution was obtained by using the method of continuity. The solution is unique if ψ_u≥0.

Key words: fully nonlinear, parabolic type, Hessian equation