WIAS Preprint No. 1834, (2013)

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



Authors

  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Reichelt, Sina
  • Thomas, Marita

2010 Mathematics Subject Classification

  • 35B25 35A01 35K57 35K65 35M10

Keywords

  • Two-scale convergence, folding and unfolding, coupled reaction-diffusion equations, nonlinear reaction, degenerating diffusion, Gronwall estimate

Abstract

We derive a two-scale homogenization limit for reaction-diffusion systems where for some species the diffusion length is of order 1 whereas for the other species the diffusion length is of the order of the periodic microstructure. Thus, in the limit the latter species will display diffusion 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.

Appeared in

  • Networks Heterogeneous Media, 9 (2014) pp. 353--382.

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