WIAS Preprint No. 2008, (2014)

Error estimates for nonlinear reaction-diffusion systems involving different diffusion length scales


  • Reichelt, Sina

2010 Mathematics Subject Classification

  • 35B25 35K57 35K65 35M10 41M25


  • Two-scale convergence, folding and unfolding, error estimates, nonlinear reaction, degenerating diffusion, Gronwall estimate




We derive quantitative error estimates for coupled reaction-diffusion systems, whose coefficient functions are quasi-periodically oscillating modeling microstructure of the underlying macroscopic domain. The coupling arises via nonlinear reaction terms, and we allow for different diffusion length scales, i.e. whereas some species have characteristic diffusion length of order 1, other species may diffuse much slower, namely, with 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.

Appeared in

  • MURPHYS-HSFS-2014: 7th MUlti-Rate Processes and HYSteresis (MURPHYS) & 2nd International Workshop on Hysteresis and Slow-Fast Systems (HSFS), O. Klein, M. Dimian, P. Gurevich, D. Knees, D. Rachinskii, S. Tikhomirov, eds., vol. 727 of Journal of Physics: Conference Series, IOP Publishing, 2016, pp. 012013/1--012013/15

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