Bistable Traveling Waves for Monotone Semiflows with Applications

TL;DR

This paper investigates the existence of bistable traveling waves in monotone evolution systems, extending results to periodic habitats and applying the theory to various classes of systems.

Contribution

It establishes a general framework for bistable traveling waves in monotone semiflows, including discrete, continuous, and periodic cases, with applications to multiple system classes.

Findings

Existence of bistable traveling waves in monotone semiflows.

Extension to periodic habitats and weak compactness cases.

Application to four classes of evolution systems.

Abstract

This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. Under an abstract setting, we establish the existence of bistable traveling waves for discrete and continuous-time monotone semiflows. This result is then extended to the cases of periodic habitat and weak compactness, respectively. We also apply the developed theory to four classes of evolution systems.