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hal.structure.identifierInsttiut for applied analysis
dc.contributor.authorDIER, Dominik
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorOUHABAZ, El Maati
dc.date.accessioned2024-04-04T02:21:07Z
dc.date.available2024-04-04T02:21:07Z
dc.date.created2013-11-06
dc.date.issued2014
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189544
dc.description.abstractEnWe 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.sponsorshipAux frontières de l'analyse Harmonique - ANR-12-BS01-0013
dc.language.isoen
dc.subject.enwave equation
dc.subject.enSesquilinear forms
dc.subject.ennon-autonomous evolution equations
dc.subject.enmaximal regularity
dc.subject.ennon-linear heat equations
dc.subject.enwave equation.
dc.title.enMaximal Regularity for Non-Autonomous Second Order Cauchy Problems
dc.typeArticle de revue
dc.identifier.doi10.1007/s00020-013-2109-6
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.identifier.arxiv1311.1902
bordeaux.journalIntegr. Eqs and Op. Theory
bordeaux.page427-450
bordeaux.volume78
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00880886
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00880886v1
bordeaux.COinSctx_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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