Periodic homogenization of strongly nonlinear reaction–diffusion equations with large reaction terms

Abstract

We study in this article 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. This study relies on a suitable version of the well-known two-scale convergence method.

Keywords:

• homogenization
• reaction–diffusion
• nonlinear

AMS Subject Classifications::

• 35B27
• 76M50

Acknowledgements

We thank the referees for several suggestions and interesting remarks.