Asymptotic stability of traveling wave fronts in the buffered bistable system

Je Chiang Tsai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


In this paper, we study a model which describes the propagation of increased calcium concentration wave front in excitable systems with the diffusing species being buffered. Our goal is to prove the global exponential stability of the unique traveling wave front. Comparing with the unbuffered system, we conclude that multiple stationary buffers (buffers do not diffuse) cannot prevent the existence of a global asymptotic stable traveling wave front, or cannot eliminate propagated waves in the buffered bistable equation. Concerning the method of the proof, we will present a method in which only the comparison principle and suitably constructed supersolutions (subsolutions) are involved. The feature of the method is to avoid calculating the spectrum of the associated linear operator.

Original languageEnglish
Pages (from-to)138-159
Number of pages22
JournalSIAM Journal on Mathematical Analysis
Issue number1
Publication statusPublished - 2007
Externally publishedYes


  • Asymptotic stability
  • Bistable equation
  • Calcium
  • FitzHugh-Nagumo equations
  • Reaction-diffusion equations
  • Traveling wave front

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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