Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations

Yong Jung Kim, Wei Ming Ni, Masaharu Taniguchi

Research output: Contribution to journalArticle

Abstract

Assume a single reaction-diüsion equation has zero as an asymp- totically stable stationary point. Then we prove that there exist no localized travelling waves with non-zero speed. If [lim infjxj!1 u(x); lim supjxj!1 u(x)] is included in an open interval of zero that does not include other stationary points, then the speed has to be zero or the travelling profile u has to be identically zero.

Original languageEnglish
Pages (from-to)3707-3718
Number of pages12
JournalDiscrete and Continuous Dynamical Systems
Volume33
Issue number8
DOIs
Publication statusPublished - Aug 2013
Externally publishedYes

Fingerprint

Reaction-diffusion Equations
Traveling Wave
Nonexistence
Stationary point
Zero
Open interval
Asymptotically Stable

Keywords

  • Reaction-diüsion equations
  • Travelling spots
  • Travelling waves

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations. / Kim, Yong Jung; Ni, Wei Ming; Taniguchi, Masaharu.

In: Discrete and Continuous Dynamical Systems, Vol. 33, No. 8, 08.2013, p. 3707-3718.

Research output: Contribution to journalArticle

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