Forced waves of reaction-diffusion model with density-dependent dispersal in shifting environments

Abstract This paper is concerned with the existence and global stability of forced waves for reaction diffusion equations with density-dependent diffusion in a shifting environment, which arises from population dynamics. Our argument is based on the introduction of suitable families of upper and lower solutions and on a comparison result through Holmgren's method. Our analysis yields, for any wave speed c > 0 , the density-dependent dispersal population models with shifting habitats admit forced traveling waves. To overcome the difficulties caused by peculiar structure of forced waves and degeneracy, we develop a novel weighted estimate technique to prove the global and exponential stability of these waves. Different from the spatial homogenous case Huang et al. 2018 [24] , the weight function is introduced near the positive equilibrium r ( + ∞ ) instead of the zero equilibrium.