Global asymptotic stability of traveling waves in delayed reaction-diffusion equations

Hal Smith, Xiao Qiang Zhao

Research output: Contribution to journalArticle

162 Scopus citations

Abstract

The existence and comparison theorem of solutions is first established for the quasimonotone delayed reaction-diffusion equations on R by appealing to the theory of abstract functional differential equations. The global asymptotic stability, Liapunov stability, and uniqueness of traveling wave solutions are then proved by the elementary super- and subsolution comparison and squeezing methods.

Original languageEnglish (US)
Pages (from-to)514-534
Number of pages21
JournalSIAM Journal on Mathematical Analysis
Volume31
Issue number3
DOIs
StatePublished - Jan 1 2000

Keywords

  • Comparison principle
  • Delayed reaction-diffusion equations
  • Super- and subsolutions
  • Traveling waves

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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