2019/06/19 by De Leenheer, Patrick, Shen, Wenxian, Zhang, Aijun
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1906.07881
This paper is devoted to the study of persistence and extinction of a species modeled by nonlocal dispersal evolution equations in moving habitats with moving speed c. It is shown that the species becomes extinct if the moving speed c is larger than the so called spreading speed c^*, where c^* is determined by the maximum linearized growth rate function. If the moving speed c is smaller than c^*, it is shown that the persistence of the species depends on the patch size of the habitat, namely, the species persists if the patch size is greater than some number L^* and in this case, there is a traveling wave solution with speed c, and it becomes extinct if the patch size is smaller than L^*.