On monostable cooperative system with nonlocal diffusion and free boundaries

TL;DR

This paper advances the understanding of monostable cooperative systems with nonlocal diffusion and free boundaries by providing precise solution estimates, analyzing semi-wave solutions, and exploring asymptotic behaviors and limiting profiles, with applications to epidemic models.

Contribution

It offers more accurate solution estimates, examines semi-wave limitations, and investigates asymptotic and limiting behaviors in nonlocal diffusion systems with free boundaries.

Findings

Enhanced solution estimates for the system.

Limitations identified for semi-wave solutions.

Asymptotic behaviors characterized for the Cauchy problem.

Abstract

This paper continues to study the monostable cooperative system with nonlocal diffusion and free boundary, which has recently been discussed by [Du and Ni, 2020, arXiv:2010.01244]. We here aim at the four aspects: the first is to give more accurate estimates for solution; the second is to discuss the limitations of solution pair of a semi-wave problem; the third is to investigate the asymptotic behaviors of the corresponding cauchy problem; the last is to study the limiting profiles of solution as one of the expanding rates of free boundary converges to $\yy$. Then two epidemic models are given to illustrate their own longtime behaviors.