Periodic Homogenization of strongly nonlinear reaction-diffusion equations with large reaction terms

TL;DR

This paper investigates the periodic homogenization of strongly nonlinear reaction-diffusion equations with large reaction terms, revealing a homogenized equation that combines reaction and convection effects, including a specific case of convection-diffusion form.

Contribution

It introduces a novel homogenization approach for nonlinear reaction-diffusion equations with large reaction terms, demonstrating the resulting equation's unique structure.

Findings

Homogenized equation combines reaction and convection effects.

In a special case, the homogenized equation is exactly convection-diffusion.

Uses a modified two-scale convergence method for analysis.

Abstract

We study in this paper the periodic homogenization problem related to a strongly nonlinear reaction-diffusion equation. Owing to the large reaction term, the homogenized equation has a rather quite different form which puts together both the reaction and convection effects. We show in a special case that, the homogenized equation is exactly of a convection-diffusion type. The study relies on a suitable version of the well-known two-scale convergence method.