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

Hal Smith, Xiao Qiang Zhao

Research output: Contribution to journalArticle

149 Citations (Scopus)

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
StatePublished - Feb 2000

Fingerprint

Liapunov Stability
Abstract Differential Equations
Supersolution
Subsolution
Squeezing
Global Asymptotic Stability
Comparison Theorem
Asymptotic stability
Functional Differential Equations
Traveling Wave Solutions
Reaction-diffusion Equations
Traveling Wave
Existence Theorem
Differential equations
Uniqueness

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics

Cite this

Global asymptotic stability of traveling waves in delayed reaction-diffusion equations. / Smith, Hal; Zhao, Xiao Qiang.

In: SIAM Journal on Mathematical Analysis, Vol. 31, No. 3, 02.2000, p. 514-534.

Research output: Contribution to journalArticle

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