Geodesic
Homogenization of a carcinogenesis model with different scalings with the homogenization parameter
Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 163-184.

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In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell. The diffusion on the endoplasmic reticulum, modeled as a Riemannian manifold, is described by the Laplace-Beltrami operator. For the binding process to the surface of the endoplasmic reticulum, different scalings with powers of the homogenization parameter are considered. This leads to three qualitatively different models in the homogenization limit.
DOI : 10.21136/MB.2014.143847
Classification : 35B10, 35B27, 35B45, 35K51, 35K58, 92C37
Keywords: periodic homogenization; two-scale convergence; carcinogenesis; reaction-diffusion system; surface diffusion 
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Graf, Isabell; Peter, Malte A. Homogenization of a carcinogenesis model with different scalings with the homogenization parameter. Mathematica Bohemica, Tome 139 (2014) no. 2, pp. 163-184. doi : 10.21136/MB.2014.143847. http://geodesic.mathdoc.fr/articles/10.21136/MB.2014.143847/

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