Uniqueness and stability of bistable waves for monotone semiflows

Abstract

This paper is devoted to the study of the uniqueness and stability of bistable traveling waves for monotone semiflows in an abstract setting. Under appropriate assumptions, we establish the uniqueness and stability of bistable waves for discrete and continuous-time semiflows in a continuous habitat by appealing to a global convergence theorem for monotone semiflows. We also extend such a result to time-periodic semiflows, and apply the general theory to a class of reaction-diffusion-advection systems in a cylinder.