Pulsating waves in a dissipative medium with Delta sources on a periodic lattice

Xinfu Chen, Xing Liang, Je Chiang Tsai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


This paper studies a dissipative heat equation with Delta sources of non-linear strength located on a periodic lattice. The model arises from intracellular waves in continuum excitable media with discrete release sites. Due to the presence of Delta sources, the solution of the model has discontinuous spatial derivatives. We focus on the bistable regime of the model, determined by the decay strength parameter a and the separation distance L between release sites, in which the model admits exactly three L-periodic steady states. We establish the existence of pulsating waves spatially connecting them. For the case of waves connecting two stable L-periodic steady states, the uniqueness and global exponential stability of pulsating waves are shown. Also a new technique is introduced to find the fine structure of the tails of pulsating waves.

Original languageEnglish
Pages (from-to)24-63
Number of pages40
JournalJournal des Mathematiques Pures et Appliquees
Publication statusPublished - 2021 Jun


  • Bistable
  • Delta function
  • Exponential stability
  • Pulsating wave

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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