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

7th International Workshop on MUlti-Rate Processes & HYSteresis; 2nd International Workshop on Hysteresis and Slow-Fast Systems

Reichelt, Sina^1

Weierstrass Institute, Mohrenstrae 39, Berlin

10117, Germany^1

关键词: Coefficient functions;    Coupled reaction-diffusion systems;    Diffusion length;    Effective systems;    Error estimates;    Macroscopic domains;    Nonlinear reaction;    Two scale convergence;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/727/1/012013/pdf
DOI  :  10.1088/1742-6596/727/1/012013

来源: IOP

【 摘 要 】

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 diffusion length scales, i.e. whereas some species have characteristic diffusion length of order 1 other species may diffuse 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.