数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 968-974.doi: 10.1016/S0252-9602(10)60094-X

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LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES

王路生1|尹景学2|王泽佳1   

  1. 1. Department of Mathematics, Jilin University, Changchun 130012, |China

    2. Department of Mathematics, South China Normal University, Guangzhou 510631, China
  • 收稿日期:2008-03-31 出版日期:2010-05-20 发布日期:2010-05-20
  • 基金资助:

    This work is supported by the NNSF of China

LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES

 WANG Lu-Sheng1, YIN Jing-Xue2, WANG Ze-Jia1   

  1. 1. Department of Mathematics, Jilin University, Changchun 130012, |China

    2. Department of Mathematics, South China Normal University, Guangzhou 510631, China
  • Received:2008-03-31 Online:2010-05-20 Published:2010-05-20
  • Supported by:

    This work is supported by the NNSF of China

摘要:

This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration
equations

|x|λ+k ∂u / ∂t =div(|x|\nabla um)+|x|λ+kup

with 0<m<1, p>1, λ ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k and k1 for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k ∈ (k, k1), otherwise, pc is infinite or does not exist.

关键词: Newtonian filtration equation, critical exponent, exterior problem, Threshold

Abstract:

This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration
equations

|x|λ+k ∂u / ∂t =div(|x|\nabla um)+|x|λ+kup

with 0<m<1, p>1, λ ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k and k1 for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k ∈ (k, k1), otherwise, pc is infinite or does not exist.

Key words: Newtonian filtration equation, critical exponent, exterior problem, Threshold

中图分类号: 

  • 35B33