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Asymptotic behaviour of a linearized water waves system in a rectangle

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorSU, Pei
dc.date.accessioned2024-04-04T02:46:47Z
dc.date.available2024-04-04T02:46:47Z
dc.date.issued2022-04
dc.identifier.issn0921-7134
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191586
dc.description.abstractEnWe consider the asymptotic behaviour of small-amplitude gravity water waves in a rectangular domain where the water depth is much smaller than the horizontal scale. The control acts on one lateral boundary, by imposing the horizontal acceleration of the water along that boundary, as a scalar input function u. The state z of the system consists of two functions: the water level ζ along the top boundary, and its time derivative ∂ζ ∂t. We prove that the solution of the water waves system converges to the solution of the one dimensional wave equation with Neumann boundary control, when taking the shallowness limit. Our approach is based on a special change of variables and a scattering semigroup, which provide the possiblity to apply the Trotter-Kato approximation theorem. Moreover, we use a detailed analysis of Fourier series for the dimensionless version of the partial Dirichlet to Neumann and Neumann to Neumann operators introduced in [1].
dc.language.isoen
dc.publisherIOS Press
dc.subject.enLinearized water waves equation
dc.subject.enDirichlet to Neumann map
dc.subject.enNeumann to Neumann map
dc.subject.enOperator semigroup
dc.subject.enTrotter-Kato theorem
dc.title.enAsymptotic behaviour of a linearized water waves system in a rectangle
dc.typeArticle de revue
dc.identifier.doi10.3233/ASY-221767
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halPhysique [physics]/Physique [physics]/Dynamique des Fluides [physics.flu-dyn]
dc.identifier.arxiv2104.00286
bordeaux.journalAsymptotic Analysis
bordeaux.page83-108
bordeaux.volume131
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03187025
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03187025v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Asymptotic%20Analysis&rft.date=2022-04&rft.volume=131&rft.issue=1&rft.spage=83-108&rft.epage=83-108&rft.eissn=0921-7134&rft.issn=0921-7134&rft.au=SU,%20Pei&rft.genre=article


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