中文摘要：

考虑抛物型k-Hessian方程-u-t＋log Sk（λ（D^2u））=φ（x,t,u）的第一初边值问题.对于一般的光滑区域Ω,在方程存在可容许下解的条件下,建立了可容许解的C（2,1）（^-QT）先验估计,并利用连续性方法得到方程可容许解的存在性.当φ_u≥0时,解是唯一的.

英文摘要：

We investigated the first initial boundary value problem of -ut＋ log Sk（λ（D2u）） =Ψ{x,t,u）,which is a class of parabolic k-Hessian equations.In the general smooth regionΩ,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