Traveling waves in a nonlocal, piecewise linear reaction-diffusion population model

E. A. Autry*, A. Bayliss, V. A. Volpert

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We consider an analytically tractable switching model that is a simplification of a nonlocal, nonlinear reaction-diffusion model of population growth where we take the source term to be piecewise linear. The form of this source term allows us to consider both the monostable and bistable versions of the problem. By transforming to a traveling frame and choosing specific kernel functions, we are able to reduce the problem to a system of algebraic equations. We construct solutions and examine the propagation speed and monotonicity of the resulting waves.

Original languageEnglish (US)
Pages (from-to)3304-3331
Number of pages28
JournalNonlinearity
Volume30
Issue number8
DOIs
StatePublished - Jul 21 2017

    Fingerprint

Keywords

  • nonlocality
  • population dynamics
  • traveling waves

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this