# American Institute of Mathematical Sciences

December  2019, 8(4): 687-694. doi: 10.3934/eect.2019032

## Simultaneous controllability of two vibrating strings with variable coefficients

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

Received  January 2018 Revised  April 2019 Published  June 2019

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.

Citation: Jamel Ben Amara, Emna Beldi. Simultaneous controllability of two vibrating strings with variable coefficients. Evolution Equations & Control Theory, 2019, 8 (4) : 687-694. doi: 10.3934/eect.2019032
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