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

作　　者：ZHAN Huashui 

机构地区：[1]School of Mathematics and Statistics,Xiamen University of Technology,Xiamen 361024,China

出　　处：《Journal of Partial Differential Equations》2024年第2期135-149,共15页偏微分方程（英文版）

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

摘　　要：The initial-boundary value problem of an anisotropic porous medium equation■is studied.Compared with the usual porous medium equation,there are two different characteristics in this equation.One lies in its anisotropic property,another one is that there is a nonnegative variable diffusion coefficient a(x,t)additionally.Since 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.

关 键 词：Anisotropic porous medium equation variable diffusion coefficient stability partial boundary condition 

分 类 号：O175.26[理学—数学]