Single input controllability of a simplified fluid-structure interaction model

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

Received: 25 March 2011
Revised: 10 August 2011

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.