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On Some Pointwise Inequalities Involving Nonlocal Operators Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Smoluchowski Equation with Variable Coefficients in Perforated Domains: Homogenization and Applications to Mathematical Models in Medicine

Authors : Bruno Franchi, Silvia Lorenzani

Published in: Harmonic Analysis, Partial Differential Equations and Applications

Publisher: Springer International Publishing

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Abstract

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 β-amyloid peptide Aβ 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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previous chapter Weighted Inequalities of Poincaré Type on Chain Domains
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Metadata
Title
Smoluchowski Equation with Variable Coefficients in Perforated Domains: Homogenization and Applications to Mathematical Models in Medicine
Authors
Bruno Franchi
Silvia Lorenzani
Copyright Year
2017
Book
Harmonic Analysis, Partial Differential Equations and Applications

Print ISBN: 978-3-319-52741-3

Electronic ISBN: 978-3-319-52742-0

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-52742-0_4

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