On the Well-Posedness Problem of the Anisotropic Porous Medium Equation with a Variable Diffusion Coefficient

作     者：ZHAN Huashui ZHAN Huashui

作者机构：School of Mathematics and StatisticsXiamen University of TechnologyXiamen 361024China 

出 版 物：《Journal of Partial Differential Equations》 (偏微分方程（英文版）)

年 卷 期：2024年第37卷第2期

页      面：135-149页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by Natural Science Foundation of Fujian Province(No.2022J011242) China 

主　　题：Anisotropic porous medium equation variable diffusion coefficient stability partial boundary condition 

摘      要：The initial-boundary value problem of an anisotropic porous medium equation■is *** with the usual porous medium equation,there are two different characteristics in this *** lies in its anisotropic property,another one is that there is a nonnegative variable diffusion coefficient a(x,t)*** a(x,t)may be degenerate on the parabolic boundary∂Ω×(0,T),instead of the boundedness of the gradient|∇u|for the usual porous medium,we can only show that∇u∈L^(∞)(0,T;L^(2)_(loc)(Ω)).Based on this property,the partial boundary value conditions matching up with the anisotropic porous medium equation are discovered and two stability theorems of weak solutions can be proved naturally.