Abstract:

We used the  prior estimation and the method of continuity to study the first initial boundary value problem of -u_tS_k(λ(D²u))=ψ(x,t,u), which is a class of parabolic k-Hessian equations, so as to obtain the existence of the admissible solutions. If the admissible subsolutions exist in general smooth region Ω, there is a prior estimation of the admissible solution. Besides, the solution is unique if ψ_u≥0.

Key words: fully nonlinear, parabolic, Hessian equations