Franchi, Bruno and Heida, Martin and Lorenzani, Silvia
(2020)
*A Mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation.*
Communications in Mathematical Sciences, 18
(4).
pp. 1105-1134.

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Official URL: DOI: https://dx.doi.org/10.4310/CMS.2020.v18.n4.a1...

## 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 |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 2345 |

Deposited By: | Silvia Hoemke |

Deposited On: | 04 Jun 2019 12:51 |

Last Modified: | 17 Jan 2022 15:21 |

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