Single input controllability of a simplified fluid-structure interaction model

Yuning Liu; Takéo Takahashi; Marius Tucsnak

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 1, page 20-42
  • ISSN: 1292-8119

Abstract

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In this paper we study a controllability problem for a simplified one dimensional model for the motion of a rigid body in a viscous fluid. The control variable is the velocity of the fluid at one end. One of the novelties brought in with respect to the existing literature consists in the fact that we use a single scalar control. Moreover, we introduce a new methodology, which can be used for other nonlinear parabolic systems, independently of the techniques previously used for the linearized problem. This methodology is based on an abstract argument for the null controllability of parabolic equations in the presence of source terms and it avoids tackling linearized problems with time dependent coefficients.

How to cite

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Liu, Yuning, Takahashi, Takéo, and Tucsnak, Marius. "Single input controllability of a simplified fluid-structure interaction model." ESAIM: Control, Optimisation and Calculus of Variations 19.1 (2013): 20-42. <http://eudml.org/doc/272791>.

@article{Liu2013,
abstract = {In this paper we study a controllability problem for a simplified one dimensional model for the motion of a rigid body in a viscous fluid. The control variable is the velocity of the fluid at one end. One of the novelties brought in with respect to the existing literature consists in the fact that we use a single scalar control. Moreover, we introduce a new methodology, which can be used for other nonlinear parabolic systems, independently of the techniques previously used for the linearized problem. This methodology is based on an abstract argument for the null controllability of parabolic equations in the presence of source terms and it avoids tackling linearized problems with time dependent coefficients.},
author = {Liu, Yuning, Takahashi, Takéo, Tucsnak, Marius},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {null-controllability; fluid-structure interaction; viscous Burgers equation; spectral methods; Carleman estimates},
language = {eng},
number = {1},
pages = {20-42},
publisher = {EDP-Sciences},
title = {Single input controllability of a simplified fluid-structure interaction model},
url = {http://eudml.org/doc/272791},
volume = {19},
year = {2013},
}

TY - JOUR
AU - Liu, Yuning
AU - Takahashi, Takéo
AU - Tucsnak, Marius
TI - Single input controllability of a simplified fluid-structure interaction model
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2013
PB - EDP-Sciences
VL - 19
IS - 1
SP - 20
EP - 42
AB - In this paper we study a controllability problem for a simplified one dimensional model for the motion of a rigid body in a viscous fluid. The control variable is the velocity of the fluid at one end. One of the novelties brought in with respect to the existing literature consists in the fact that we use a single scalar control. Moreover, we introduce a new methodology, which can be used for other nonlinear parabolic systems, independently of the techniques previously used for the linearized problem. This methodology is based on an abstract argument for the null controllability of parabolic equations in the presence of source terms and it avoids tackling linearized problems with time dependent coefficients.
LA - eng
KW - null-controllability; fluid-structure interaction; viscous Burgers equation; spectral methods; Carleman estimates
UR - http://eudml.org/doc/272791
ER -

References

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