Homogenization for Time-periodic KPP Reactions

TL;DR

This paper establishes homogenization results for time-periodic reaction-advection-diffusion equations with KPP reactions in ergodic settings, providing explicit formulas and extending to non-local diffusion models.

Contribution

It introduces a homogenization framework for time-periodic KPP reactions, including explicit formulas and extensions to non-local diffusion.

Findings

Homogenization proven for time-periodic KPP reaction-diffusion equations.

Explicit formula derived for the homogenized dynamics.

Results extended to non-local diffusion models.

Abstract

We prove homogenization for reaction-advection-diffusion equations with KPP reactions, in the time-periodic spatially stationary ergodic setting, and find an explicit formula for the homogenized dynamic. We also extend this result to models with non-local diffusion and KPP reactions.