Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (3): 531-542.

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Extinction and Non-Extinction Behavior of Solutions for a Class of Reaction-Diffusion Equations with a Nonlinear Source

Zhou Sen1,2, Yang Zuodong1,3   

  1. 1 Institute of Mathematics, College of Science and Mathematics, Nanjing Normal University, Nanjing 210023;
    2 College of Sciences, China Pharmaceutical University, Nanjing 211198;
    3 School of Teacher Education, Nanjing Normal University, Nanjing 210097
  • Received:2015-11-03 Revised:2016-03-24 Online:2016-06-26 Published:2016-06-26
  • Supported by:

    Supported by the NSFC (11571093, 11471164)

Abstract:

In this paper, we investigate the extinction and nonextinction behavior of solutions for a class of reaction-diffusion equations. By using the integral model estimates and the method of sub-super solutions, we obtain some sufficient conditions for the solutions vanish in finite time. Furthermore, we also present numerical examples for the sake of illustration.

Key words: Reaction-diffusion equation, Nonlinear source, Extinction, Non-extinction

CLC Number: 

  • O175.29
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