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Maximal Regularity for Evolution Equations Governed by Non-Autonomous Forms
| hal.structure.identifier | Insttiut for applied analysis | |
| dc.contributor.author | ARENDT, Wolfgang | |
| hal.structure.identifier | Insttiut for applied analysis | |
| dc.contributor.author | DIER, Dominik | |
| hal.structure.identifier | Département de Mathématiques | |
| dc.contributor.author | LAASRI, Hafida | |
| hal.structure.identifier | Équipe Analyse | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T02:18:10Z | |
| dc.date.available | 2024-04-04T02:18:10Z | |
| dc.date.created | 2013-01-10 | |
| dc.date.issued | 2014 | |
| dc.identifier.issn | 1079-9389 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189290 | |
| dc.description.abstractEn | \begin{abstract}\label{abstract} We consider a non-autonomous evolutionary problem \[ \dot{u} (t)+\A(t)u(t)=f(t), \quad u(0)=u_0 \] where the operator $\A(t):V\to V^\prime$ is associated with a form $\fra(t,.,.):V\times V \to \R$ and $u_0\in V$. Our main concern is to prove well-posedness with maximal regularity which means the following. Given a Hilbert space $H$ such that $V$ is continuously and densely embedded into $H$ and given $f\in L^2(0,T;H)$ we are interested in solutions $u \in H^1(0,T;H)\cap L^2(0,T;V)$. We do prove well-posedness in this sense whenever the form is piecewise Lipschitz-continuous and symmetric. Moreover, we show that each solution is in $C([0,T];V)$. 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.publisher | Khayyam Publishing | |
| 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.title.en | Maximal Regularity for Evolution Equations Governed by Non-Autonomous Forms | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 1303.1166 | |
| bordeaux.journal | Advances in Differential Equations | |
| bordeaux.page | ??? | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00797181 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00797181v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Advances%20in%20Differential%20Equations&rft.date=2014&rft.spage=???&rft.epage=???&rft.eissn=1079-9389&rft.issn=1079-9389&rft.au=ARENDT,%20Wolfgang&DIER,%20Dominik&LAASRI,%20Hafida&OUHABAZ,%20El%20Maati&rft.genre=article |
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