The Uniform Spreading Speed in Cooperative Systems with Non-Uniform Initial Data

Ru Hou, Zhian Wang, Wen Bing Xu, Zhitao Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper considers the spreading speed of cooperative nonlocal dispersal systems with irreducible reaction functions and non-uniform initial data. Here the non-uniformity means that all components of initial data decay exponentially but their decay rates are different. It is well-known that in a monostable reaction-diffusion or nonlocal dispersal equation, different decay rates of initial data yield different spreading speeds. In this paper, we show that due to the cooperation and irreducibility of reaction functions, all components of the solution with non-uniform initial data will possess a uniform spreading speed which decreasingly depends only on the smallest decay rate of initial data. The decreasing property of the uniform spreading speed in the smallest decay rate further implies that the component with the smallest decay rate can accelerate the spatial propagation of other components.

Original languageEnglish
Pages (from-to)585-601
Number of pages17
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume17
Issue number2
DOIs
Publication statusPublished - Feb 2024

Keywords

  • cooperative systems
  • exponential decay
  • initial data function
  • Nonlocal dispersal
  • spreading speeds

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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