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

2021/09/30 by Alfaro, Matthieu, Xiao, Dongyuan · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.15074

Abstract

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 "faster" species excludes the "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 \itbump phenomenon.

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• Non-Monotone Traveling Waves of the Weak Competition Lotka-Volterra System
• Controllability of diffusive Lotka-Volterra strongly competitive systems under boundary constrained controls

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