The logarithmic delay of KPP fronts in a periodic medium

TL;DR

This paper extends Bramson's logarithmic delay result for KPP fronts from constant to periodic reaction rates, showing that the lag between solutions and traveling waves grows as (3/2) log(t).

Contribution

It generalizes the known delay growth from constant to periodic reaction rates in KPP equations, providing a broader understanding of wave propagation in periodic media.

Findings

The lag between solutions and traveling waves grows as (3/2) log(t) in periodic media.

The result confirms the universality of Bramson's delay in more complex environments.

The analysis applies to solutions with compactly supported initial data.

Abstract

We consider solutions of the KPP-type equations with a periodically varying reaction rate, and compactly supported initial data. It has been shown by M. Bramson in the case of the constant reaction rate that the lag between the position of such solutions and that of the traveling waves grows as (3/2) log(t). We generalize this result to the periodic case