### Electronic Research Archive

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

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

• 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.

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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• 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.

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