Self-similar behaviour of a non-local diffusion equation with time delay
| hal.structure.identifier | Université Le Havre Normandie [ULH] | |
| dc.contributor.author | DUCROT, Arnaud | |
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | GENADOT, Alexandre | |
| dc.date.accessioned | 2024-04-04T03:02:38Z | |
| dc.date.available | 2024-04-04T03:02:38Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193006 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.subject.en | Non-local diffusion | |
| dc.subject.en | Time delay | |
| dc.subject.en | Self-similar behaviour | |
| dc.subject.en | Fractional Sobolev estimates | |
| dc.subject.en | Central Limit Theorem | |
| dc.title.en | Self-similar behaviour of a non-local diffusion equation with time delay | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1812.11342 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01964356 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01964356v1 | |
| bordeaux.COinS | ctx_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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