数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (1): 79-96.doi: 10.1016/S0252-9602(16)30117-5

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THE POINTWISE ESTIMATES OF SOLUTIONS FOR A NONLINEAR CONVECTION DIFFUSION REACTION EQUATION

刘国威   

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
  • 收稿日期:2015-10-28 修回日期:2016-04-29 出版日期:2017-02-25 发布日期:2017-02-25
  • 作者简介:Guowei LIU,E-mail:guoweiliu19881203@163.com

THE POINTWISE ESTIMATES OF SOLUTIONS FOR A NONLINEAR CONVECTION DIFFUSION REACTION EQUATION

Guowei LIU   

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2015-10-28 Revised:2016-04-29 Online:2017-02-25 Published:2017-02-25
  • About author:Guowei LIU,E-mail:guoweiliu19881203@163.com

摘要:

This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension. First, the pointwise estimates of solutions are obtained, furthermore, we obtain the optimal Lp, 1≤p≤+∞, convergence rate of solutions for small initial data. Then we establish the local existence of solutions, the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data. Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.

关键词: convection diffusion reaction equation, pointwise estimate, Green function, energy method

Abstract:

This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension. First, the pointwise estimates of solutions are obtained, furthermore, we obtain the optimal Lp, 1≤p≤+∞, convergence rate of solutions for small initial data. Then we establish the local existence of solutions, the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data. Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.

Key words: convection diffusion reaction equation, pointwise estimate, Green function, energy method