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Single input controllability of a simplified fluid-structure interaction model

Published online by Cambridge University Press:  23 February 2012

Yuning Liu,
Takéo Takahashi and
Marius Tucsnak
Yuning Liu
Affiliation:
Institut Elie Cartan, Nancy Université/CNRS/INRIA, BP 70239, 54506 Vandoeuvre-lès-Nancy, France. liuyuning.math@gmail.com; takeo8@gmail.com; Marius.Tucsnak@iecn.u-nancy.fr
Takéo Takahashi
Affiliation:
Institut Elie Cartan, Nancy Université/CNRS/INRIA, BP 70239, 54506 Vandoeuvre-lès-Nancy, France. liuyuning.math@gmail.com; takeo8@gmail.com; Marius.Tucsnak@iecn.u-nancy.fr
Marius Tucsnak
Affiliation:
Institut Elie Cartan, Nancy Université/CNRS/INRIA, BP 70239, 54506 Vandoeuvre-lès-Nancy, France. liuyuning.math@gmail.com; takeo8@gmail.com; Marius.Tucsnak@iecn.u-nancy.fr

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.

Keywords

Null-controllabilityfluid-structure interactionviscous Burgers equation

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 1 , January 2013, pp. 20 - 42
Copyright
© EDP Sciences, SMAI, 2012

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