Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (3): 802-814.doi: 10.1016/S0252-9602(16)30041-8

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STABILITY OF TIME-PERIODIC TRAVELING FRONTS IN BISTABLE REACTION-ADVECTION-DIFFUSION EQUATIONS

Weijie SHENG   

  1. Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, China
  • Received:2015-03-13 Revised:2015-05-28 Online:2016-06-25 Published:2016-06-25
  • Supported by:

    This work was supported by National Natural Science Foundation of China (11401134), China Postdoctoral Science Foundation Funded Project (2012M520716), the Fundamental Research Funds for the Central Universities (HIT.NSRIF.2014063)

Abstract:

This paper is concerned with the global exponential stability of time periodic traveling fronts of reaction-advection-diffusion equations with time periodic bistable nonlinearity in infinite cylinders. It is well known that such traveling fronts exist and are asymptotically stable. In this paper, we further show that such fronts are globally exponentially stable. The main difficulty is to construct appropriate supersolutions and subsolutions.

Key words: stability, reaction-advection-diffusion equations, bistable, time periodic traveling fronts

CLC Number: 

  • 35B35
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