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Strong stability for a fluid–structure interaction model
Author(s) -
GrobbelaarVan Dalsen Marié
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1104
Subject(s) - resolvent , dissipative system , compressibility , mathematics , fluid–structure interaction , interface model , stability (learning theory) , mathematical analysis , shear (geology) , mechanics , classical mechanics , physics , computer science , thermodynamics , materials science , human–computer interaction , finite element method , machine learning , composite material
In this paper we consider the question of stabilization of a fluid–structure model that describes the interaction between a 3‐D incompressible fluid and a 2‐D plate, the interface, which coincides with a flat flexible part of the surface of the vessel containing the fluid. The mathematical model comprises the Stokes equations and the equations for the longitudinal deflections of the plate with inclusion of the shear stress, which the fluid exerts on the plate. We show that the energy associated with the model decays strongly when the interface is equipped with a locally supported dissipative mechanism. Our main tool is an abstract resolvent criterion due to Tomilov. Copyright © 2008 John Wiley & Sons, Ltd.