Varying the direction of propagation in reaction-diffusion equations in periodic media

TL;DR

This paper investigates how the speed and profile of reaction-diffusion fronts in periodic media vary continuously with the direction of propagation, ensuring uniform spreading properties across all directions.

Contribution

It establishes the continuous dependence of pulsating front speeds and profiles on propagation direction in multidimensional periodic media.

Findings

Propagation speed depends continuously on direction.

Profiles are unique and vary continuously with direction.

Spreading properties are uniform across all directions.

Abstract

We consider a multidimensional reaction-diffusion equation of either ignition or monostable type, involving periodic heterogeneity, and analyze the dependence of the propagation phenomena on the direction. We prove that the (minimal) speed of the underlying pulsating fronts depends continuously on the direction of propagation, and so does its associated profile provided it is unique up to time shifts. We also prove that the spreading properties \cite{Wein02} are actually uniform with respect to the direction.