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Self-similar behaviour of a non-local diffusion equation with time delay

hal.structure.identifierUniversité Le Havre Normandie [ULH]
dc.contributor.authorDUCROT, Arnaud
hal.structure.identifierQuality control and dynamic reliability [CQFD]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorGENADOT, Alexandre
dc.date.accessioned2024-04-04T03:02:38Z
dc.date.available2024-04-04T03:02:38Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193006
dc.description.abstractEnWe study the asymptotic behaviour of solutions of a class of linear non-local measure-valued differential equations with time delay. Our main result states that the solutions asymptotically exhibit a parabolic like behaviour in the large times, that is precisely expressed in term of heat kernel. Our proof relies on the study of a-self-similar-rescaled family of solutions. We first identify the asymptotic behaviour of the solutions by deriving a convergence result in the sense of the Young measures. Then we strengthen this convergence by deriving suitable fractional Sobolev compactness estimates. As a by-product, our main result allows to obtain asymptotic results for a class of piecewise constant stochastic processes with memory.
dc.language.isoen
dc.subject.enNon-local diffusion
dc.subject.enTime delay
dc.subject.enSelf-similar behaviour
dc.subject.enFractional Sobolev estimates
dc.subject.enCentral Limit Theorem
dc.title.enSelf-similar behaviour of a non-local diffusion equation with time delay
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Systèmes dynamiques [math.DS]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv1812.11342
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01964356
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01964356v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=DUCROT,%20Arnaud&GENADOT,%20Alexandre&rft.genre=preprint


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