Error Estimates For Nonlinear Reaction-Diffusion Systems Involving Different Diffusion Length Scales

We derive quantitative error estimates for coupled reaction-diffusion systems, whose coefficient functions are quasi-periodically oscillating modeling the microstructure of the underlying macroscopic domain. The coupling arises via nonlinear reaction terms and we allow for different di ff usion length scales, i. e. whereas some species have characteristic di ff usion length of order 1 other species may di ff use with the order of the characteristic microstructure-length scale. We consider an effective system, which is rigorously obtained via two-scale convergence, and we derive quantitative error estimates.