Sharp estimates for the spreading speeds of the Lotka-Volterra competition-diffusion system: The strong-weak type with pushed front

Chang Hong Wu; Dongyuan Xiao; Maolin Zhou

doi:10.1016/j.matpur.2023.02.004

Sharp estimates for the spreading speeds of the Lotka-Volterra competition-diffusion system: The strong-weak type with pushed front

Chang Hong Wu, Dongyuan Xiao^*, Maolin Zhou

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the classical two-species Lotka-Volterra competition-diffusion system in the strong-weak competition case. When the corresponding minimal speed of the traveling waves is nonlinearly selected, we show that the solution of the Cauchy problem uniformly converges to the minimal traveling wave in two different situations, for which the invading speed is locally determined: (i) one species is an invasive one and the other is a native species; (ii) both two species are invasive species.

Original language	English
Pages (from-to)	236-264
Number of pages	29
Journal	Journal des Mathematiques Pures et Appliquees
Volume	172
DOIs	https://doi.org/10.1016/j.matpur.2023.02.004
State	Published - Apr 2023

Keywords

Cauchy problem
Competition-diffusion system
Long-time behavior
Traveling waves

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10.1016/j.matpur.2023.02.004

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abstract = "We consider the classical two-species Lotka-Volterra competition-diffusion system in the strong-weak competition case. When the corresponding minimal speed of the traveling waves is nonlinearly selected, we show that the solution of the Cauchy problem uniformly converges to the minimal traveling wave in two different situations, for which the invading speed is locally determined: (i) one species is an invasive one and the other is a native species; (ii) both two species are invasive species.",

keywords = "Cauchy problem, Competition-diffusion system, Long-time behavior, Traveling waves",

author = "Wu, {Chang Hong} and Dongyuan Xiao and Maolin Zhou",

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AB - We consider the classical two-species Lotka-Volterra competition-diffusion system in the strong-weak competition case. When the corresponding minimal speed of the traveling waves is nonlinearly selected, we show that the solution of the Cauchy problem uniformly converges to the minimal traveling wave in two different situations, for which the invading speed is locally determined: (i) one species is an invasive one and the other is a native species; (ii) both two species are invasive species.

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KW - Competition-diffusion system

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KW - Traveling waves

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Sharp estimates for the spreading speeds of the Lotka-Volterra competition-diffusion system: The strong-weak type with pushed front

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Keywords

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