Exact controllability of a beam in an incompressible inviscid fluid

Scott W. Hansen; Andrei A. Lyashenko

doi:10.3934/dcds.1997.3.59

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1997, Volume 3, Issue 1: 59-78. Doi: 10.3934/dcds.1997.3.59

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Exact controllability of a beam in an incompressible inviscid fluid

Scott W. Hansen^1, and
Andrei A. Lyashenko^2,

1.
Department of Mathematics, Iowa State University, Ames, IA 50011
2.
Department of Mathemtics, University of Illinois at Chicago, Chicago, IL 60607

Received: April 30, 1996

Published: December 1996

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Abstract

It is well known that an Euler-Bernoulli beam may be exactly controlled with a single control acting on an end of the beam. In this article we show that for certain boundary conditions, the same result holds for a beam that is surrounded by an incompressible, inviscid fluid with a sufficiently small density. The proof involves reducing the control problem to a moment problem and using compactness properties of the Neumann to Dirichlet map for the Laplacian operator to obtain the needed estimates.

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Mathematics Subject Classification: 93C20, 73K05, 76B40.

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