Global existence and uniqueness of solutions for one-dimensional reaction-interface systems

Yan Yu Chen, Hirokazu Ninomiya, Chang Hong Wu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we provide a mathematical framework in studying the wave propagation with the annihilation phenomenon in excitable media. We deal with the existence and uniqueness of solutions to a one-dimensional free boundary problem (called a reaction–interface system) arising from the singular limit of a FitzHugh–Nagumo type reaction–diffusion system. Because of the presence of the annihilation, interfaces may intersect each other. We introduce the notion of weak solutions to study the continuation of solutions beyond the annihilation time. Under suitable conditions, we show that the free boundary problem is well-posed.

Original languageEnglish
Pages (from-to)102-130
Number of pages29
JournalJournal of Differential Equations
Volume324
DOIs
StatePublished - 5 Jul 2022

Keywords

  • Excitable system
  • Free boundary problem
  • Reaction-interface system
  • Singular limit
  • Weak solutions

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