Simultaneous controllability of two vibrating strings with variable coefficients

Jamel Ben Amara; Emna Beldi

doi:10.3934/eect.2019032

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2019, Volume 8, Issue 4: 687-694. Doi: 10.3934/eect.2019032

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Simultaneous controllability of two vibrating strings with variable coefficients

Jamel Ben Amara^1, and
Emna Beldi^2,

1.
University of Tunis El Manar, Faculty of Sciences of Tunis, Tunisia
2.
University of Carthage, Polytechnic School of Tunisia, Tunisia

Received: December 31, 2017

Revised: March 31, 2019

Early access: June 2019

Published: June 2019

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Abstract

We study the simultaneous exact controllability of two vibrating strings with variable physical coefficients and controlled from a common endpoint. We give sufficient conditions on the physical coefficients for which the eigenfrequencies of both systems do not coincide and the associated spectral gap is uniformly positive. Under these conditions, we show that these systems are simultaneously exactly controllable.

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Mathematics Subject Classification: 93B, 35P.

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References

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