| Autor: |
Franchi, Bruno, Heida, Martin, Lorenzani, Silvia |
| Rok vydání: |
2019 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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