一类与时间有关的非线性椭圆抛物型方程解的存在性

The Existence of Solution to a Class of Nonlinear Elliptic Parabolic Equation with Time

本文讨论了在更为一般的Lp空间上,利用Yosida逼近和凸函数的标准正则化将问题两次离散化,进而求出变形后方程的解,最后对其解进行一致性估计和取极限,就证明了原问题的解,这种解更具有一般性。

The article investigates the solution to the problem on the more general Lp space. First, using the Yosida approximation and the standard regularization of the convex function it makes problem t discreted twicely, and then finds out the solution to discretization equation and finally consistency estimates to the solution and takes limit. It proves that the solution of original problem and the solution is more general.