一类拟线性退缩抛物方程的双相自由边界问题

A DOUBLE-PHASE FREE BOUNDARY PROBLEM FOR QUASI-LINEAR DEGENERATE PARABOLIC EQUATIONS

本文研究了形如(1.1)～(1.4)的拟线性退缩抛物方程的双相自由边界问题。使用极值原理和 Schauder 不动点原理,证明了正则化问题解的存在性。在对正则化问题的解做了一些必要的估计的基础上,证明了广义解的存在性,最后,也讨论了广义解的唯一性。

In this paper,we study the double-phase free boundary problem forquasilinear degenerate parabolic equations of the type(1.1)—(1.4).At first,using Schauder fixed point theorem and maximum principle,we prove the existence and the uniqueness for the solutions of reqularizedproblems.Then,we make the necessary estimates for the solutions.On thebasis of this,the existence of generalized solutions is obtained by the meansof the parabolic reqularzation.Finally,we also discuss the uniqueness ofgeneralized solutions.