Asymptotic behavior for the fast diffusion equation with absorption and singularity

被引：0

作者：

Xie, Changping ^{[1
,4
]}

Fang, Shaomei ^{[1
]}

Mei, Ming ^{[2
,3
,4
]}

Qin, Yuming ^{[5
,6
]}

机构：

[1] South China Agr Univ, Coll Math & Informat, Guangzhou 510642, Guangdong, Peoples R China

[2] Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Jiangxi, Peoples R China

[3] Champlain Coll, Dept Math, St Lambert, PQ J4P 3P2, Canada

[4] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

[5] Donghua Univ, Inst Nonlinear Sci, Shanghai 200051, Peoples R China

[6] Donghua Univ, Sch Math & Stat, Shanghai 200051, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2025年 / 414卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Fast diffusion; Decay estimate; Asymptotic behavior; Generalized Shannon's inequality; Entropy dissipation method; POROUS-MEDIA EQUATION; LARGE TIME BEHAVIOR; BLOW-UP; STABILITY; EXISTENCE;

D O I：

10.1016/j.jde.2024.09.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the weak solution for the fast diffusion equation with absorption and singularity in the form of u(t) = Delta u(m) - u(p). We first prove the existence and decay estimate of weak solution when the fast diffusion index satisfies 0 < m < 1 and the absorption index is p > 1. Then we show the asymptotic convergence of weak solution to the corresponding Barenblatt solution for n-1/n < m < 1 and p > m + 2/n via the entropy dissipation method combining the generalized Shannon's inequality and Csisz & aacute;r-Kullback inequality. The singularity of spatial diffusion causes us the technical challenges for the asymptotic behavior of weak solution. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页码：722 / 745

页数：24

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