Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion

We derive a two-scale homogenization limit for reaction-di usion systems where for some species the di usion length is of order 1 whereas for the other species the di usion length is of the order of the periodic microstructure. Thus, in the limit the latter species will display di usion only on the microscale but not on the macroscale. Because of this missing compactness, the nonlinear coupling through the reaction terms cannot be homogenized but needs to be treated on the two-scale level. In particular, we have to develop new error estimates to derive strong convergence results for passing to the limit.