数学物理学报(英文版)

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ON THE STABILITY OF THE POSITIVE RADIAL STEADY STATES FOR A SEMILINEAR CAUCHY PROBLEM INVOLVING CRITICAL EXPONENTS

邓引斌; 杨芬   

  1. 华中师范大学数学与统计学院, 武汉 430079
  • 收稿日期:2005-10-18 修回日期:2006-08-21 出版日期:2008-04-20 发布日期:2008-04-20
  • 通讯作者: 邓引斌
  • 基金资助:
    The research supported by the National Natural Science Foundation of China
    (10471052, 10631030) and the PHD specialized grant of Ministry of Education of China (20060511001)

ON THE STABILITY OF THE POSITIVE RADIAL STEADY STATES FOR A SEMILINEAR CAUCHY PROBLEM INVOLVING CRITICAL EXPONENTS

Deng Yinbin; Yang Fen   

  1. Department of Mathematics, Huazhong Normal University, Wuhan 430079, China
  • Received:2005-10-18 Revised:2006-08-21 Online:2008-04-20 Published:2008-04-20
  • Contact: Deng Yinbin

摘要: This article is contributed to the Cauchy problem
$$ \left\{\begin{array}{ll} \D
\frac{\partial u}{\partial t}=
\Delta u+K( |x|)u^p \ \ \mbox{in} \ R^n \times(0,T),\\
u(x,0)=\varphi(x) \ \ \mbox{in} \ R^n ;
\end{array}
\right. $$
with initial function $\varphi \not \equiv 0$. The stability of positive radial steady state, which are positive solutions of △u+K( | x|)up=0, is obtained when p is critical for general K(|x|).

关键词: Stability, Cauchy problem, asymptotic stability

Abstract: This article is contributed to the Cauchy problem
$$ \left\{\begin{array}{ll} \D
\frac{\partial u}{\partial t}=
\Delta u+K( |x|)u^p \ \ \mbox{in} \ R^n \times(0,T),\\
u(x,0)=\varphi(x) \ \ \mbox{in} \ R^n ;
\end{array}
\right. $$
with initial function $\varphi \not \equiv 0$. The stability of positive radial steady state, which are positive solutions of △u+K( | x|)up=0, is obtained when p is critical for general K(|x|).

Key words: Stability, Cauchy problem, asymptotic stability

中图分类号: 

  • 35J10