Abstract

We consider the reaction-diffusion competition system in the so-called critical competition case. The associated ODE system then admits infinitely many equilibria, which makes the analysis intricate. We first prove the nonexistence of 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 spreading speed), but also provide a sharp description of the profile of the solution, thus shedding light on a new bump phenomenon.

中文翻译：

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Lotka–Volterra 竞争扩散系统：关键竞争案例

摘要

我们在所谓的临界竞争案例中考虑反应扩散竞争系统。关联的 ODE 系统然后允许无限多个平衡点，这使得分析变得复杂。我们首先通过应用相平面分析证明不存在最终单调行波。接下来，我们研究具有紧支撑初始数据的 Cauchy 问题解的大时间行为。我们不仅揭示了“更快”的物种排除了“更慢”的物种（具有已知的传播速度），而且还提供了对溶液轮廓的清晰描述，从而揭示了一种新的颠簸现象。