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dc.contributor.authorCarrillo, José A.
dc.contributor.authorGonzález Nogueras, María del Mar
dc.contributor.authorGualdani, Maria
dc.contributor.authorSchonbek, Maria E.
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.description.abstractIn this paper we analyze the global existence of classical solutions to the initial boundaryvalue problem for a nonlinear parabolic equation describing the collective behavior of an ensemble of neurons. These equations were obtained as a diffusive approximation of the mean-field limit of a stochastic differential equation system. The resulting Fokker-Planck equation presents a nonlinearity in the coeffcients depending on the probability ux through the boundary. We show by an appropriate change of variables that this parabolic equation with nonlinear boundary conditions can be transformed into a non standard Stefan-like free boundary problem with a source term given by a delta function. We prove that there are global classical solutions for inhibitory neural networks, while for excitatory networks we give local well-posedness of classical solutions together with a blow up criterium. Finally, we will also study ....
dc.format.extent22 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshDifferential equations, Nonlinear
dc.titleClassical solutions for a nonlinear Fokker-Planck equation arising in computational neuroscience
dc.typeExternal research report
dc.subject.lemacEquacions diferencials parabòliques
dc.subject.lemacEquacions diferencials no lineals
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.rights.accessOpen Access

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