Approximate controllability for a linear model of fluid structure interaction

Axel Osses; Jean-Pierre Puel

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 4, page 497-513
  • ISSN: 1292-8119

Abstract

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We consider a linear model of interaction between a viscous incompressible fluid and a thin elastic structure located on a part of the fluid domain boundary, the other part being rigid. After having given an existence and uniqueness result for the direct problem, we study the question of approximate controllability for this system when the control acts as a normal force applied to the structure. The case of an analytic boundary has been studied by Lions and Zuazua in [9] where, in particular, a counterexample is given when the fluid domain is a ball. We prove a result of approximate controllability in the 2d-case when the rigid and the elastic parts of the boundary make a rectangular corner and if the control acts on the whole elastic structure.

How to cite

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Osses, Axel, and Puel, Jean-Pierre. "Approximate controllability for a linear model of fluid structure interaction." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 497-513. <http://eudml.org/doc/197380>.

@article{Osses2010,
abstract = { We consider a linear model of interaction between a viscous incompressible fluid and a thin elastic structure located on a part of the fluid domain boundary, the other part being rigid. After having given an existence and uniqueness result for the direct problem, we study the question of approximate controllability for this system when the control acts as a normal force applied to the structure. The case of an analytic boundary has been studied by Lions and Zuazua in [9] where, in particular, a counterexample is given when the fluid domain is a ball. We prove a result of approximate controllability in the 2d-case when the rigid and the elastic parts of the boundary make a rectangular corner and if the control acts on the whole elastic structure. },
author = {Osses, Axel, Puel, Jean-Pierre},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Controllability; fluid-structure interaction; nonsmooth domains; unique continuation property.; unique continuation property; eigenvalue problem},
language = {eng},
month = {3},
pages = {497-513},
publisher = {EDP Sciences},
title = {Approximate controllability for a linear model of fluid structure interaction},
url = {http://eudml.org/doc/197380},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Osses, Axel
AU - Puel, Jean-Pierre
TI - Approximate controllability for a linear model of fluid structure interaction
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 497
EP - 513
AB - We consider a linear model of interaction between a viscous incompressible fluid and a thin elastic structure located on a part of the fluid domain boundary, the other part being rigid. After having given an existence and uniqueness result for the direct problem, we study the question of approximate controllability for this system when the control acts as a normal force applied to the structure. The case of an analytic boundary has been studied by Lions and Zuazua in [9] where, in particular, a counterexample is given when the fluid domain is a ball. We prove a result of approximate controllability in the 2d-case when the rigid and the elastic parts of the boundary make a rectangular corner and if the control acts on the whole elastic structure.
LA - eng
KW - Controllability; fluid-structure interaction; nonsmooth domains; unique continuation property.; unique continuation property; eigenvalue problem
UR - http://eudml.org/doc/197380
ER -

References

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  11. A. Osses and J.-P. Puel, Approximate controllability of a linear model in solid-fluid interaction in a rectangle. to appear.  Zbl0919.35019
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