Stabilizability properties of a linearized water waves system
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | SU, Pei | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | TUCSNAK, Marius | |
| hal.structure.identifier | Tel Aviv University [TAU] | |
| dc.contributor.author | WEISS, George | |
| dc.date.accessioned | 2024-04-04T02:55:15Z | |
| dc.date.available | 2024-04-04T02:55:15Z | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 0167-6911 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192345 | |
| dc.description.abstractEn | We consider the strong stabilization of small amplitude gravity water waves in a two dimensional rectangular domain. The control acts on one lateral boundary, by imposing the horizontal acceleration of the water along that boundary, as a multiple of a scalar input function $u$, times a given function $h$ of the height along the active boundary. The state $z$ of the system consists of two functions: the water level $\zeta$ along the top boundary, and its time derivative $\dot\zeta$. We prove that for suitable functions $h$, there exists a bounded feedback functional $F$ such that the feedback $u=Fz$ renders the closed-loop system strongly stable. Moreover, for initial states in the domain of the semigroup generator, the norm of the solution decays like $(1+t)^{-\frac{1}{6}}$. Our approach uses a detailed analysis of the partial Dirichlet to Neumann and Neumann to Neumann operators associated to certain edges of the rectangular domain, as well as recent abstract non-uniform stabilization results by Chill, Paunonen, Seifert, Stahn and Tomilov (2019). | |
| dc.description.sponsorship | Ecoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure - ANR-18-CE40-0027 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | strong stabilization | |
| dc.subject.en | state feedback | |
| dc.subject.en | Neumann to Neumann map | |
| dc.subject.en | Dirichlet to Neumann map | |
| dc.subject.en | Linearized water waves equation | |
| dc.subject.en | Hilbert's inequality | |
| dc.subject.en | operator semigroup | |
| dc.subject.en | collocated actuators and sensors | |
| dc.title.en | Stabilizability properties of a linearized water waves system | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.sysconle.2020.104672 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.subject.hal | Physique [physics]/Physique [physics]/Dynamique des Fluides [physics.flu-dyn] | |
| dc.identifier.arxiv | 2003.10123 | |
| bordeaux.journal | Systems and Control Letters | |
| 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-02458379 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02458379v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Systems%20and%20Control%20Letters&rft.date=2020&rft.eissn=0167-6911&rft.issn=0167-6911&rft.au=SU,%20Pei&TUCSNAK,%20Marius&WEISS,%20George&rft.genre=article |
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