Traveling waves in integro-difference equations with a shifting habitat

Abstract We study an integro-difference equation that describes the spatial dynamics of a species in a shifting habitat. The growth function is nondecreasing in density and space for a given time, and shifts at a constant speed c. The spreading speeds for the model were previously studied. The contribution of the current paper is to provide sharp conditions for existence of forced traveling waves with speed c. We show the existence of traveling waves with zero value at ∞ or −∞ for c in different value ranges determined by the spreading speeds. We also show the existence of a traveling wave with any speed c for the case that the species can grow everywhere. Our results demonstrate the existence of different types of traveling waves with the same speed.

• Publication year

  2020

• Venue

  Journal of Differential Equations

• Publication date

  2020-03-15

• Fields of study

  Mathematics, Environmental Science

• Identifiers
  DOI 10.1016/j.jde.2019.10.018
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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