CLASSIFICATION OF SELF-SIMILAR SOLUTIONS OF THE DEGENERATE POLYTROPIC FILTRATION EQUATIONS  

作　　者：Zhipeng LIU Shanming JI 刘志鹏;季善明

机构地区：[1]School of Mathematics,South China University of Technology,Guangzhou 510641,China

出　　处：《Acta Mathematica Scientia》2025年第2期615-635,共21页数学物理学报(B辑英文版)

基　　金：supported by the NSFC(12271178,12171166);the Guangzhou Basic and Applied Basic Research Foundation(2024A04J2022);the TCL Young Scholar(2024-2027).

摘　　要：In this paper,we study the self-similar solutions of the degenerate diffusion equation ut-div(|▽u^(m)|^(p-2)▽u^(m))=0 of polytropic filtration diffusion in R^(N)×(0,±∞)or(R^(N)/{0})×(0,±∞)with N≥1,m>0,p>1,such that m(p-1)>1.We give a clear classification of the self-similar solutions of the form u(x,t)=(βt)^(-α/β)((βt)^(-1/β)|x|)withα∈R andβ=α[m(p-1)-1]+p,regular or singular at the origin point.The existence and uniqueness of some solutions are established by the phase plane analysis method,and the asymptotic properties of the solutions near the origin and the infinity are also described.This paper extends the classical results of self-similar solutions for degeneratep-Laplace heat equation by Bidaut-Véron[Proc Royal Soc Edinburgh,2009,139:1-43]to the doubly nonlinear degenerate diffusion equations.

关 键 词：self-similar solutions polytropic filtration equation degenerate diffusion equation doubly nonlinear diffusion 

分 类 号：O175.2[理学—数学]