关于渗流方程古典解存在性的一个注记

本文考虑具耗散项的渗流方程的第一初边值问题整体古典解存在性问题,指出了文[1]中所用Galerkin方法的不完整性,用抛物正则化方法完成了在一定条件下古典解存在性的证明。

A Note on the Existence of Classical Solutions for the Filtration Equation with Absorption

This paper is devoted to the global existence of classical solutions of the first boundary value problem for the filtration equation with absorption. The similar question has ever been considered in [1] based on the Galerkin method, but the proff is incomplete. After pointing out the incompleteness, the paper deals with the global existence of classical solutions under the smallness condition for the initial data by the method of parabolic regularization instead of the Galerkin method.