# American Institute of Mathematical Sciences

March  2004, 11(2&3): 311-324. doi: 10.3934/dcds.2004.11.311

## Controllability properties of a vibrating string with variable axial load

 1 Department of Mathematics, Washington State University, Pullman, WA 99164-3113, United States

Received  October 2002 Revised  February 2004 Published  June 2004

We show that the set of equilibrium-like states $(y_d, 0)$ of a vibrating string which can approximately be reached in the energy space $H_0^1 (0,1) \times L^2 (0,1)$ from almost any non-zero initial datum by varying its axial load is dense in the subspace $H_0^1 (0,1) \times$ {0} of this space. Our result is based on a constructive argument and makes use of piecewise constant-in-time control functions (loads) only, which enter the model equation as coefficients.
Citation: Alexander Khapalov. Controllability properties of a vibrating string with variable axial load. Discrete & Continuous Dynamical Systems, 2004, 11 (2&3) : 311-324. doi: 10.3934/dcds.2004.11.311
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