# Sharp Asymptotics for KPP Pulsating Front Speed-up and Diffusion Enhancement by Flows

## TL;DR

This paper investigates how periodic incompressible flows can accelerate KPP front speeds and enhance effective diffusivity, providing asymptotic limits for these quantities as flow strength increases.

## Contribution

It establishes the existence and asymptotic behavior of minimal front speed and effective diffusivity in the presence of strong periodic flows.

## Key findings

- Limit of minimal front speed divided by flow strength as A→∞
- Limit of effective diffusivity divided by flow strength squared as A→∞
- Quantitative characterization of flow-induced front speed-up and diffusion enhancement

## Abstract

We study KPP pulsating front speed-up and effective diffusivity enhancement by general periodic incompressible flows. We prove the existence of and determine the limits $c^*(A)/A$ and $D(A)/A^2$ as $A\to\infty$, where $c^*(A)$ is the minimal front speed and $D(A)$ the effective diffusivity.