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

• 论文 • 上一篇    下一篇

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

尹景学|王良伟|黄锐   

  1. 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   

  1. 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:

In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with
absorption utumup=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(RN), there exists an initial-value u0C(RN) with limx→∞u0(x)=0 such that φ is an ω-limit point of the rescaled solutions t u/2u(β, t), where β=2-u(m-1)/4.

关键词: complexity, asymptotic behavior, porous medium equation

Abstract:

In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with
absorption utumup=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(RN), there exists an initial-value u0C(RN) with limx→∞u0(x)=0 such that φ is an ω-limit point of the rescaled solutions t u/2u(β, t), where β=2-u(m-1)/4.

Key words: complexity, asymptotic behavior, porous medium equation

中图分类号: 

  • 35B40