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- W4288366236 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 $beta$-amyloid peptide (A$beta$) 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 A$beta$ in the monomeric form at the level of neuronal membranes." @default.
- W4288366236 created "2022-07-29" @default.
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- W4288366236 date "2019-04-18" @default.
- W4288366236 modified "2023-09-26" @default.
- W4288366236 title "A Mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation" @default.
- W4288366236 doi "https://doi.org/10.48550/arxiv.1904.11015" @default.
- W4288366236 hasPublicationYear "2019" @default.
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