The purpose of this paper is to investigate asymptotic behaviors of the solutions for a competition system with random vs.nonlocal dispersal.We first prove the existence of invasion traveling waves via using the theor...The purpose of this paper is to investigate asymptotic behaviors of the solutions for a competition system with random vs.nonlocal dispersal.We first prove the existence of invasion traveling waves via using the theory of asymptotic speeds of spread.Then we prove the invasion traveling waves are exponentially stable as perturbation in some exponentially weighted spaces by using the weighted energy and the squeezing technique.展开更多
This paper is concerned with stability of traveling wave fronts for nonlocal diffusive system.We adopt L^(1),-weighted,L^(1)-and L^(2)-energy estimates for the perturbation systems,and show that all solutions of...This paper is concerned with stability of traveling wave fronts for nonlocal diffusive system.We adopt L^(1),-weighted,L^(1)-and L^(2)-energy estimates for the perturbation systems,and show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave fronts provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev spaces.展开更多
基金Natural Science Foundation of Shanghai(No.18ZR1426500).
文摘The purpose of this paper is to investigate asymptotic behaviors of the solutions for a competition system with random vs.nonlocal dispersal.We first prove the existence of invasion traveling waves via using the theory of asymptotic speeds of spread.Then we prove the invasion traveling waves are exponentially stable as perturbation in some exponentially weighted spaces by using the weighted energy and the squeezing technique.
基金supported by the China Postdoctoral Science Foundation(No.2020M670963)supported by the Natural Science Foundation of China(No.12071297)the Natural Science Foundation of Shanghai(No.18ZR1426500).
文摘This paper is concerned with stability of traveling wave fronts for nonlocal diffusive system.We adopt L^(1),-weighted,L^(1)-and L^(2)-energy estimates for the perturbation systems,and show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave fronts provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev spaces.
