Existence, uniqueness and stability of traveling wavefronts for nonlocal dispersal equations with convolution type bistable nonlinearity

Abstract

This article concerns the bistable traveling wavefronts of a nonlocal dispersal equation with convolution type bistable nonlinearity. Applying a homotopy method, we establish the existence of traveling wavefronts. If the wave speed does not vanish, i.e. $c\neq 0$, then the uniqueness (up to translation) and the globally asymptotical stability of traveling wavefronts are proved by the comparison principle and squeezing technique.

Keywords

• Nonlocal dispersal
• traveling wavefronts
• bistable nonlinearity
• continuation method
• squeezing technique