The Bramson delay in a Fisher–KPP equation with log-singular nonlinearity

Emeric Bouin, Christopher Henderson

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider a class of reaction–diffusion equations of Fisher–KPP type in which the nonlinearity (reaction term) f is merely C1 at u=0 due to a logarithmic competition term. We first derive the asymptotic behavior of (minimal speed) traveling wave solutions that is, we obtain precise estimates on the decay to zero of the traveling wave profile at infinity. We then use this to characterize the Bramson shift between the traveling wave solutions and solutions of the Cauchy problem with localized initial data. We find a phase transition depending on how singular f is near u=0 with quite different behavior for more singular f. This is in contrast to the smooth case, that is, when f∈C1,δ, where these behaviors are completely determined by f(0). In the singular case, several scales appear and require new techniques to understand.

Original languageEnglish (US)
Article number112508
JournalNonlinear Analysis, Theory, Methods and Applications
Volume213
DOIs
StatePublished - Dec 2021
Externally publishedYes

Keywords

  • Logarithmic delay
  • Reaction–diffusion equations
  • Traveling waves

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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