Stability of forced traveling waves for a nonlocal dispersal Lotka-Volterra cooperation system under shifting habitat

This paper is concerned with the globally exponential stability of forced traveling waves for a nonlocal dispersal Lotka-Volterra cooperation system under shifting habitats. It was shown in a recent work (Hu et al., 2021 [11]) that this system admits a forced traveling wave provided that the forcing speed is positive. In this paper, we further study the globally asymptotic stability of forced traveling waves. By applying the weighted energy method together with the comparison principle and Fourier's transform, we prove that the forced traveling waves with relatively large speeds are globally asymptotically stable in the weighted Banach spaces provided that the initial perturbations of the forced traveling waves also belong to the same spaces.