Controllability properties of a vibrating string with variable axial load

Alexander Khapalov

doi:10.3934/dcds.2004.11.311

Article Contents

2004, Volume 11, Issue 2&3: 311-324. Doi: 10.3934/dcds.2004.11.311

This issue Previous Article Smale diffeomorphisms of surfaces: a classification algorithm Next Article Coupled map lattices without cluster expansion

Controllability properties of a vibrating string with variable axial load

Alexander Khapalov^1,

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

Received: October 2002

Revised: February 2004

Published: September 2004

Abstract Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: 93, 35.

Citation:

Article Metrics

HTML views() PDF downloads(77) Cited by(0)

Controllability properties of a vibrating string with variable axial load

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Controllability properties of a vibrating string with variable axial load

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content