A mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2595 | |
dc.contributor.author | Franchi, Bruno | |
dc.contributor.author | Heida, Martin | |
dc.contributor.author | Lorenzani, Silvia | |
dc.date.accessioned | 2022-06-23T09:38:50Z | |
dc.date.available | 2022-06-23T09:38:50Z | |
dc.date.issued | 2019 | |
dc.description.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. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9169 | |
dc.identifier.uri | https://doi.org/10.34657/8207 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2595 | |
dc.relation.hasversion | https://doi.org/10.4310/CMS.2020.v18.n4.a10 | |
dc.relation.issn | 2198-5855 | |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | |
dc.subject.other | Smoluchowski equation | eng |
dc.subject.other | stochastic homogenization | eng |
dc.subject.other | Alzheimer disease | eng |
dc.title | A mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 31 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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