Displaying similar documents to “Approximate controllability for a linear model of fluid structure interaction”

Exact controllability in fluid – solid structure: The Helmholtz model

Jean-Pierre Raymond, Muthusamy Vanninathan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability...

Single input controllability of a simplified fluid-structure interaction model

Yuning Liu, Takéo Takahashi, Marius Tucsnak (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

Local null controllability of a two-dimensional fluid-structure interaction problem

Muriel Boulakia, Axel Osses (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we prove a controllability result for a fluid-structure interaction problem. In dimension two, a rigid structure moves into an incompressible fluid governed by Navier-Stokes equations. The control acts on a fixed subset of the fluid domain. We prove that, for small initial data, this system is null controllable, that is, for a given , the system can be driven at rest and the structure to its reference configuration at time . To show this result, we first consider a linearized system....

Boundary exact controllability for a porous elastic Timoshenko system

Manoel J. Santos, Carlos A. Raposo, Leonardo R. S. Rodrigues (2020)

Applications of Mathematics

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In this paper, we consider a one-dimensional system governed by two partial differential equations. Such a system models phenomena in engineering, such as vibrations in beams or deformation of elastic bodies with porosity. By using the HUM method, we prove that the system is boundary exactly controllable in the usual energy space. We will also determine the minimum time allowed by the method for the controllability to occur.