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. 143. (Unpublished)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 coagulationdiffusion equations with nonhomogeneous Neumann boundary conditions. This system is meant to model the aggregation and diffusion of βamyloid 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 nonperiodicity of the cellular structure of the brain by assuming a stochastic model for the spatial distribution of neurons. Further, we consider nonperiodic 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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