On monostable cooperative system with nonlocal diffusion and free boundaries

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.