Asymptotic spreading in a delayed dispersal predator-prey system without comparison principle

Shuxia Pan; Shuxia Pan

doi:10.3934/era.2019011

Electronic Research Archive

2019, Volume 27, 89-99. doi: 10.3934/era.2019011

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Asymptotic spreading in a delayed dispersal predator-prey system without comparison principle

Shuxia Pan

School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received: 01 September 2019 Revised: 01 December 2019
Primary: 35K57, 37C65; Secondary: 92D25

This paper deals with the initial value problem of a predator-prey system with dispersal and delay, which does not admit the classical comparison principle. When the initial value has nonempty compact support, the initial value problem formulates that two species synchronously invade the same habitat in population dynamics. By constructing proper auxiliary equations and functions, we confirm the faster invasion speed of two species, which equals to the minimal wave speed of traveling wave solutions in earlier works.
- Upper-lower solutions,
- asymptotic spreading,
- nonmonotone system
Citation: Shuxia Pan. Asymptotic spreading in a delayed dispersal predator-prey system without comparison principle[J]. Electronic Research Archive, 2019, 27: 89-99. doi: 10.3934/era.2019011

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Abstract

This paper deals with the initial value problem of a predator-prey system with dispersal and delay, which does not admit the classical comparison principle. When the initial value has nonempty compact support, the initial value problem formulates that two species synchronously invade the same habitat in population dynamics. By constructing proper auxiliary equations and functions, we confirm the faster invasion speed of two species, which equals to the minimal wave speed of traveling wave solutions in earlier works.

References

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