一类抛物型方程的粘性解

Viscosity solutions for a class of parabolic equations

讨论一类退化、奇异抛物型方程的初边值问题 .通过构造上下解 ,利用粘性解的比较原理和 Per-ron方法 。

In this paper the initial and Dirichlet problem for a class of degenerate and singular nonlinear parabolic equations were investigated. This problem was derived from the evolution of a parametric surface by its mean curvature subject to fixed boundary conditions. The existence and uniqueness of viscosity solutions by constructing subsolutions and supersolutions were proved.