The formation of spreading front: the singular limit of three-component reaction–diffusion models

Hirofumi Izuhara, Harunori Monobe, Chang Hong Wu

Research output: Contribution to journalArticlepeer-review

Abstract

Understanding the invasion processes of biological species is a fundamental issue in ecology. Several mathematical models have been proposed to estimate the spreading speed of species. In recent decades, it was reported that some mathematical models of population dynamics have an explicit form of the evolution equations for the spreading front, which are represented by free boundary problems such as the Stefan-like problem (e.g., Mimura et al., Jpn J Appl Math 2:151–186, 1985; Du and Lin, SIAM J Math Anal 42:377–405, 2010). To understand the formation of the spreading front, in this paper, we will consider the singular limit of three-component reaction–diffusion models and give some interpretations for spreading front from the viewpoint of modeling. As an application, we revisit the issue of the spread of the grey squirrel in the UK and estimate the spreading speed of the grey squirrel based on our result. Also, we discuss the relation between some free boundary problems related to population dynamics and mathematical models describing Controlling Invasive Alien Species. Lastly, we numerically consider the traveling wave solutions, which give information on the spreading behavior of invasive species.

Original languageEnglish
Article number38
JournalJournal of Mathematical Biology
Volume82
Issue number5
DOIs
Publication statusPublished - Apr 2021

Keywords

  • Free boundary problems
  • Reaction–diffusion systems
  • Singular limit
  • Spreading front
  • Traveling waves

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'The formation of spreading front: the singular limit of three-component reaction–diffusion models'. Together they form a unique fingerprint.

Cite this