Show simple item record

dc.contributor.authorWillie, R.
dc.contributor.authorWacher, A.
dc.date.accessioned2017-02-21T08:18:18Z
dc.date.available2017-02-21T08:18:18Z
dc.date.issued2013-12-31
dc.identifier.issn1938-9787
dc.identifier.urihttp://hdl.handle.net/20.500.11824/530
dc.description.abstractIn this paper, we study the well-posedness in scales of Hilbert spaces Eα, α ∈ ℝ defined by the non-coupled system partial differential operator of a chemotaxis model of aggregation of microglia in Alzheimer's disease for a perturbated analytic semigroup, which decays exponentially in the large time asymptotic dynamics of the problem to a finite dimensional set K ⊂ ℝ3 of the spatial average solutions. Uniform bounds in Ω × (0, T) of solutions and gradient solutions to the system of equations are proved. Thus via a bootstrap argument solutions to the problem are shown to be classical solutions. Furthermore, under natural conditions on the coupled elliptic system quasilinear differential operator, we prove the existence of a fundamental solution or evolution operator for the model equations in cited function spaces. In conclusion numerical simulation results are provided.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectAggregation of microglia
dc.subjectAlzeheimer's disease
dc.subjectChemotaxis Model
dc.subjectNumerical simulation
dc.subjectUniform bounds
dc.titleAnalysis and numerical simulations of a chemotaxis model of aggregation of microglia in Alzheimer's disease
dc.typeinfo:eu-repo/semantics/articleen_US
dc.relation.publisherversionhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84885069512&partnerID=40&md5=19940f765e4fa674c36272645e5eea54
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US
dc.journal.titleCommunications in Mathematical Analysisen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España