临界三物种竞争扩散系统：行波刚性与最快物种选择
Critical Three-Species Competition-Diffusion: Traveling-Wave Rigidity and the Fastest-Species Selection
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中文总结 AI 辅助
针对一维临界三物种竞争扩散系统，研究行波刚性与长期物种选择，结合熵方法及相关不等式，在特定条件下可使较慢物种灭绝并收敛至最快物种的平衡点。
中文摘要 AI 辅助
我们研究一维临界三物种竞争扩散系统中行波的刚性及长期物种选择问题。针对临界单纯形上连接不同平衡点的行波，我们建立了若干刚性结果。当某一物种的Fisher-KPP扩散速度严格大于另外两个物种时，结合Gagliardo-Nirenberg不等式与Nash不等式的熵方法，可使较慢物种均匀灭绝，且在所有速度低于其KPP速度的锥内收敛至最快物种的平衡点。
英文摘要
We study the rigidity of traveling waves and long-time species selection in a one-dimensional critical three-species competition-diffusion system. We establish several rigidity results for traveling waves connecting distinct equilibria on the critical simplex. In the case where one species has a strictly larger Fisher-KPP spreading speed than the other two, an entropy method, combined with Gagliardo-Nirenberg and Nash inequalities yieldsuniform extinction of the slower species and convergence to the fastest-species equilibrium throughout every cone with speed below its KPP speed.
