Transition fronts for inhomogeneous Fisher-KPP reactions and non-local diffusion

TL;DR

This paper establishes the existence and construction of transition fronts in reaction-diffusion equations with spatially varying Fisher-KPP reactions and non-local diffusion, extending previous methods to more complex diffusion types.

Contribution

It introduces a novel approach to construct transition fronts for inhomogeneous Fisher-KPP equations with non-local diffusion, expanding the applicability of existing linearization techniques.

Findings

Proved existence of transition fronts in inhomogeneous Fisher-KPP equations.

Constructed solutions as perturbations of linearized PDE solutions.

Extended classical diffusion methods to non-local diffusion cases.

Abstract

We prove existence of and construct transition fronts for a class of reaction- diffusion equations with spatially inhomogeneous Fisher-KPP type reactions and non-local diffusion. Our approach is based on finding these solutions as perturbations of appropriate solutions to the linearization of the PDE at zero. Our work extends a method introduced by one of us to study such questions in the case of classical diffusion.