Journal
HARMONIC ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS: IN HONOR OF RICHARD L. WHEEDEN
Volume -, Issue -, Pages 49-67Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/978-3-319-52742-0_4
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In this paper, we study the homogenization of a Smoluchowski system of periodic discrete diffusion-coagulation equations, when the diffusion coefficients depend on all variables, in particular on the microscopic variable. This system modelizes the aggregation and diffusion of the beta-amyloid peptide A beta(42) in the cerebral tissue, a process associated with the development of Alzheimer's disease. Our homogenization result, based on Allaire-Nguetseng two-scale convergence, is meant to pass from a microscopic model to a macroscopic one.
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