Spatial propagation in nonlocal dispersal Fisher-KPP equations

Wen Bing Xu, Wan Tong Li, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we focus on three problems about the spreading speeds of nonlocal dispersal Fisher-KPP equations. First, we study the signs of spreading speeds and find that they are determined by the asymmetry level of the nonlocal dispersal and f(0), where f is the reaction function. This indicates that asymmetric dispersal can influence the spatial dynamics in three aspects: it can determine the spatial propagation directions of solutions, influence the stability of equilibrium states, and affect the monotone property of solutions. Second, we give an improved proof of the spreading speed result by constructing new lower solutions and using the new “forward-backward spreading” method. Third, we investigate the relationship between spreading speed and exponentially decaying initial data. Our result demonstrates that when dispersal is symmetric, spreading speed decreases along with the increase of the exponential decay rate. In addition, the results on the signs of spreading speeds are applied to two special cases where we present more details on the influence of asymmetric dispersal.

Original languageEnglish (US)
Article number108957
JournalJournal of Functional Analysis
Volume280
Issue number10
DOIs
StatePublished - May 15 2021

Keywords

  • Asymmetric kernel
  • Nonlocal dispersal Fisher-KPP equation
  • Spatial propagation
  • Spreading speed

ASJC Scopus subject areas

  • Analysis

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