Existence and nonexistence of traveling waves for a nonlocal monostable equation

TL;DR

This paper investigates the conditions under which traveling wave solutions exist or do not exist for a nonlocal Fisher-KPP type equation, extending classical results to more general measures.

Contribution

It provides new sufficient and necessary conditions for the existence of traveling waves in a nonlocal setting without assuming absolute continuity of the measure.

Findings

Established a sufficient condition for the existence of traveling waves.

Derived a necessary condition for the existence of periodic traveling waves.

Extended classical results to nonlocal equations with general measures.

Abstract

We consider the nonlocal analogue of the Fisher-KPP equation. We do not assume that the Borel-measure is absolutely continuous with respect to the Lebesgue measure. We gives a sufficient condition for existence of traveling waves, and a necessary condition for existence of periodic traveling waves.