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Article Dans Une Revue Communications in Partial Differential Equations Année : 2023

Lotka-Volterra competition-diffusion system: the critical competition case

Résumé

We consider the reaction-diffusion competition system in the so-called {\it critical competition case}. The associated ODE system then admits infinitely many equilibria, which makes the analysis intricate. We first prove the non-existence of {\it ultimately monotone} traveling waves by applying the phase plane analysis. Next, we study the large time behavior of the solution of the Cauchy problem with a compactly supported initial datum. We not only reveal that the \lq\lq faster'' species excludes the \lq\lq slower'' one (with a known {\it spreading speed}), but also provide a sharp description of the profile of the solution, thus shedding light on a new {\it{bump phenomenon}}.
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Dates et versions

hal-03359377 , version 1 (30-09-2021)

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Matthieu Alfaro, Dongyuan Xiao. Lotka-Volterra competition-diffusion system: the critical competition case. Communications in Partial Differential Equations, 2023, ⟨10.48550/arXiv.2109.15074⟩. ⟨hal-03359377⟩
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