8 papers
Critical Three-Species Competition-Diffusion: Traveling-Wave Rigidity and the Fastest-Species Selection
Haozhe Shu, Dongyuan Xiao
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 res…
Propagation Direction of Bistable Traveling Fronts in the Lotka--Volterra Competition--Diffusion System
Shizhao Ma, Dongyuan Xiao, Maolin Zhou
We study the propagation direction of bistable traveling fronts in the two-species Lotka--Volterra competition--diffusion system under strong competition. A complete characterizati…
Sharp logarithmic corrections for a strong-weak Lotka-Volterra competition system
Hongjun Guo, Dongyuan Xiao, Maolin Zhou
We study the one-dimensional strong-weak Lotka-Volterra competition-diffusion system \[ u_t=u_{xx}+u(1-u-av),\qquad v_t=dv_{xx}+rv(1-v-bu), \] with compactly supported initial data…
Complete Classification of Traveling Waves and Resolution of Linear Conjecture in Monostable Systems
Changhong Wu, Dongyuan Xiao, Maolin Zhou
In this paper, we present a complete classification of traveling wave solutions for monostable systems within a unified framework. To this end, we introduce a novel technique, refe…
Linear vs. nonlinear speed selection of the front propagation into unstable states
Chang-Hong Wu, Dongyuan Xiao, Maolin Zhou
In this paper, we mainly consider the speed selection problem for the classical Lotka-Volterra competition system. For the first time, we propose a sufficient and necessary conditi…
The Bramson correction in the Fisher-KPP equation: from delay to advance
Matthieu Alfaro, Thomas Giletti, Dongyuan Xiao
We consider the solution to the scalar Fisher-KPP equation with front-like initial data, focusing on the location of its level sets at large times, particularly their deviation fro…