数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1875-1882.doi: 10.1016/S0252-9602(12)60146-5

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EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A SINGULAR PARABOLIC EQUATION

夏莉1|李敬娜2|姚正安3   

  1. 1. Department of Mathematics, Shenzhen University, Shenzhen 518060, China;
    2. Department of Mathematics, Jinan University, Guangzhou 510632, China;
    3. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
  • 收稿日期:2011-03-01 修回日期:2011-07-13 出版日期:2012-09-20 发布日期:2012-09-20
  • 基金资助:

    Supported by Natural Science Foundation of Youth and Tianyuan (11001177, 11026156, 10926141) and Startup Program of Shenzhen University.

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A SINGULAR PARABOLIC EQUATION

 XIA Li1, LI Jing-Na2, YAO Zheng-An3   

  1. 1. Department of Mathematics, Shenzhen University, Shenzhen 518060, China;
    2. Department of Mathematics, Jinan University, Guangzhou 510632, China;
    3. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
  • Received:2011-03-01 Revised:2011-07-13 Online:2012-09-20 Published:2012-09-20
  • Supported by:

    Supported by Natural Science Foundation of Youth and Tianyuan (11001177, 11026156, 10926141) and Startup Program of Shenzhen University.

摘要:

In this paper, we study the initial-boundary value problem for a class of sin-gular parabolic equations. Under some conditions, we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regularization method and the sub-super solutions method. As a byproduct, we prove the existence of solutions to some problems with gradient terms, which blow up on the boundary.

关键词: existence, singular parabolic equation, asymptotic behavior

Abstract:

In this paper, we study the initial-boundary value problem for a class of sin-gular parabolic equations. Under some conditions, we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regularization method and the sub-super solutions method. As a byproduct, we prove the existence of solutions to some problems with gradient terms, which blow up on the boundary.

Key words: existence, singular parabolic equation, asymptotic behavior

中图分类号: 

  • 35K15