COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION

doi:10.1016/S0252-9602(10)60179-8

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (6): 1865-1880.doi: 10.1016/S0252-9602(10)60179-8

COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION

尹景学|王良伟|黄锐

Department of Mathematics, Jilin University, Changchun 130012, China；School of Mathematical Sciences, South China Normal University, Guangzhou 510031, China

收稿日期:2010-04-14 出版日期:2010-11-20 发布日期:2010-11-20
基金资助:
This work is partially supported by National Natural Science Foundation of China, partially supported by Specialized Research Fund for the Doctoral Program of Higher Education, and partially supported by Graduate Innovation Fund of Jilin University (20101045).

COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION

YIN Jing-Xue, WANG Liang-Wei, HUANG Rui

Department of Mathematics, Jilin University, Changchun 130012, China；School of Mathematical Sciences, South China Normal University, Guangzhou 510031, China

Received:2010-04-14 Online:2010-11-20 Published:2010-11-20
Supported by:
This work is partially supported by National Natural Science Foundation of China, partially supported by Specialized Research Fund for the Doctoral Program of Higher Education, and partially supported by Graduate Innovation Fund of Jilin University (20101045).

摘要/Abstract

摘要：

In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with
absorption u_t-Δu^m+γu^p=0, where γ≥0, m>1and p>m+2/N. We will show that if γ=0 and 0<μ<2N/N(m-1)+2, or γ>0 and 1/p-1<μ<2N/N(m-1)+2, then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S(R^N), there exists an initial-value u₀∈C(R^N) with lim_x→∞u₀(x)=0 such that φ is an ω-limit point of the rescaled solutions t ^u/²u(t ^β, t), where β=2-u(m-1)/4.

关键词: complexity, asymptotic behavior, porous medium equation

Abstract:

Key words: complexity, asymptotic behavior, porous medium equation

中图分类号:

35B40

尹景学, 王良伟, 黄锐. COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION[J]. 数学物理学报(英文版), 2010, 30(6): 1865-1880.

YIN Jing-Xue, WANG Liang-Wei, HUANG Rui. COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION[J]. Acta mathematica scientia,Series B, 2010, 30(6): 1865-1880.

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COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION

COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION

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