系数退化的拟线性抛物方程解的存在性

Existence of Solutions to Quasilinear Parabolic Equation with Coefficient Degeneracy

本文主要研究了一类系数退化的拟线性抛物方程解的存在性。首先利用Rothe方法,将所研究的问题离散化,转化成椭圆问题。进一步利用变分法给出椭圆问题解的存在性。其次构造了两类逼近解,且利用先验估计和弱收敛方法给出退化系数具有正下界时拋物问题解的存在性。最后,利用抛物正则化方法以及先验估计,给出所研究问题解的存在性。

In this paper, we mainly study existence of solutions of quasilinear parabolic equations with coefficient degeneracy. Firstly, we discrete the problem into elliptic problems by using the the Rothe method .Secondly,we prove the existence of solution of theelliptic problem with the variational method. Then we construct two types of approximation solutions, and use the priori estimates and weak convergence method to prove out the existence of solutions of parabolic equations with coefficient degeneracy thathas a positive lower bound.Finally, using the parabolic regularization method and priori estimates ,we give proof of existence of solu- tion of the given parabolic problem.