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Maximal Regularity for Non-Autonomous Second Order Cauchy Problems
| hal.structure.identifier | Insttiut for applied analysis | |
| dc.contributor.author | DIER, Dominik | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T02:21:07Z | |
| dc.date.available | 2024-04-04T02:21:07Z | |
| dc.date.created | 2013-11-06 | |
| dc.date.issued | 2014 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189544 | |
| dc.description.abstractEn | We consider non-autonomous wave equations \[ \left\{ \begin{aligned} &\ddot u(t) + \B(t)\dot u(t) + \A(t)u(t) = f(t) \quad t\text{-a.e.}\\ &u(0)=u_0,\, \dot u(0) = u_1. \end{aligned} \right. \] where the operators $\A(t)$ and $\B(t)$ are associated with time-dependent sesquilinear forms $\fra(t,.,.)$ and $\frb$ defined on a Hilbert space $H$ with the same domain $V$. The initial values satisfy $ u_0 \in V$ and $u_1 \in H$. We prove well-posedness and maximal regularity for the solution both in the spaces $V'$ and $H$. We apply the results to non-autonomous Robin-boundary conditions and also use maximal regularity to solve a quasilinear problem. | |
| dc.description.sponsorship | Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013 | |
| dc.language.iso | en | |
| dc.subject.en | wave equation | |
| dc.subject.en | Sesquilinear forms | |
| dc.subject.en | non-autonomous evolution equations | |
| dc.subject.en | maximal regularity | |
| dc.subject.en | non-linear heat equations | |
| dc.subject.en | wave equation. | |
| dc.title.en | Maximal Regularity for Non-Autonomous Second Order Cauchy Problems | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00020-013-2109-6 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 1311.1902 | |
| bordeaux.journal | Integr. Eqs and Op. Theory | |
| bordeaux.page | 427-450 | |
| bordeaux.volume | 78 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00880886 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00880886v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Integr.%20Eqs%20and%20Op.%20Theory&rft.date=2014&rft.volume=78&rft.issue=3&rft.spage=427-450&rft.epage=427-450&rft.au=DIER,%20Dominik&OUHABAZ,%20El%20Maati&rft.genre=article |
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