Stabilization of a fluid structure interaction with nonlinear damping

• Autorzy: Lasiecka I. , Lu Y.
• Języki publikacji: EN

Abstrakty

EN

Asymptotic stability of finite energy solutions to a fluid-structure interaction with a static interface in a bounded domain Ω ∈ Rⁿ, n = 2 is considered. It is shown that the undamped model subject to ”partial flatness” geometric condition on the in- terface produces solutions whose energy converges strongly to zero; while with a stress type feedback control applied on the interface of the structure, the model produces solutions whose energy is exponentially stable. An addition of a static damping on the interface produces solutions whose full norm in the phase space is exponentially stable. Without a static damping an interesting phenomenon occurs that steady state solutions (equilibria) might generate genuinely growing in time solutions. This is purely nonlinear phenomenon captured by newly developed techniques amenable to handle instability of steady state solutions arising from nonlinearity.

Słowa kluczowe

EN

fluid structure interaction; interface; Navier-Stokes equation; system of elasticity; feedback boundary control; strong stability; uniform stability; optimal control; passive damping; active damping; dynamic and static damping

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: Vol. 42, no. 1
• Strony: 155--181
• Opis fizyczny: Bibliogr. 36 poz.

Twórcy

autor

Lasiecka I.

• Department of Mathematics, University of Virginia Charlottesville, VA 22904, USA
• Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland

autor

Lu Y.

• Department of Mathematics and Computer Science, Virginia State University Petersburg, VA 23806, USA

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