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dc.contributor.authorWillie, R.
dc.contributor.authorWacher, A.
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.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_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.journal.titleCommunications in Mathematical Analysisen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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