Doubly nonlocal Fisher-KPP equation: Speeds and uniqueness of traveling waves

TL;DR

This paper investigates traveling wave solutions for a reaction-diffusion equation with nonlocal anisotropic diffusion and mixed local-nonlocal reactions, establishing relations between wave speeds, profiles, and proving their uniqueness up to shifts.

Contribution

It introduces a novel analysis of traveling waves in a nonlocal anisotropic setting, including speed-profile relations and uniqueness results.

Findings

Relations between wave speeds and profiles are characterized.

Uniqueness of traveling wave profiles up to shifts is proved.

The study advances understanding of nonlocal reaction-diffusion equations.

Abstract

We study traveling waves for a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions. We describe relations between speeds and asymptotic of profiles of traveling waves, and prove the uniqueness of the profiles up to shifts.