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January  1997, 3(1): 59-78. doi: 10.3934/dcds.1997.3.59

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, United States
2. 

Department of Mathemtics, University of Illinois at Chicago, Chicago, IL 60607, United States

Received  May 1996 Published  October 1996

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.
Keywords: Exact controllability, ideal fluid., Euler-Bernoulli beam.
Mathematics Subject Classification: 93C20, 73K05, 76B4.
Citation: Scott W. Hansen, Andrei A. Lyashenko. Exact controllability of a beam in an incompressible inviscid fluid. Discrete and Continuous Dynamical Systems, 1997, 3 (1) : 59-78. doi: 10.3934/dcds.1997.3.59
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