American Institute of Mathematical Sciences

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

Exact controllability of a beam in an incompressible inviscid fluid

 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.
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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