Existence of traveling wave solutions for a nonlocal bistable equation: an abstract approach

TL;DR

This paper proves the existence of monotone traveling wave solutions for a nonlocal bistable equation using an abstract recursive method, without assuming absolute continuity of the measure.

Contribution

It introduces a novel recursive approach for abstract monotone dynamical systems to establish traveling wave solutions in nonlocal equations.

Findings

Existence of monotone traveling wave solutions proven

Applicable to equations with non-absolutely continuous measures

Develops a new recursive method for abstract systems

Abstract

We consider traveling fronts to the nonlocal bistable equation. We do not assume that the Borel-measure is absolutely continuous with respect to the Lebesgue measure. We show that there is a traveling wave solution with monotone profile. In order to prove this result, we would develop a recursive method for abstract monotone dynamical systems and apply it to the equation.