Repository: Freie Universität Berlin, Math Department

A Mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation

Franchi, B. and Heida, M. and Lorenzani, S. (2019) A Mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation. SFB 1114 Preprint in arXiv:1904.11015 . pp. 1-43. (Unpublished)

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Official URL: https://arxiv.org/abs/1904.11015

Abstract

In this note, we apply the theory of stochastic homogenization to find the asymptotic behavior of the solution of a set of Smoluchowski's coagulation-diffusion equations with non-homogeneous Neumann boundary conditions. This system is meant to model the aggregation and diffusion of β-amyloid peptide (Aβ) in the cerebral tissue, a process associated with the development of Alzheimer's disease. In contrast to the approach used in our previous works, in the present paper we account for the non-periodicity of the cellular structure of the brain by assuming a stochastic model for the spatial distribution of neurons. Further, we consider non-periodic random diffusion coefficients for the amyloid aggregates and a random production of Aβ in the monomeric form at the level of neuronal membranes.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:2345
Deposited By: Silvia Hoemke
Deposited On:04 Jun 2019 12:51
Last Modified:04 Jun 2019 12:51

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