Summary
We consider the problem of simultaneously controlling two elastic string by means of a control acting on an arbitrarily small region of the strings. We show that, when the densities of the strings are different, the system is exactly controllable in any time larger than the characteristic times of the strings. When the densities coincides, the answer is similar to the case of simultaneous control from one end of the strings: in this case the controllability properties depend on the rational approximation properties of the ratio of the lengths.
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References
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Dáger, R. (2003). Simultaneous Interior Controllability of Elastic Strings. In: Cohen, G.C., Joly, P., Heikkola, E., Neittaanmäki, P. (eds) Mathematical and Numerical Aspects of Wave Propagation WAVES 2003. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55856-6_32
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DOI: https://doi.org/10.1007/978-3-642-55856-6_32
Publisher Name: Springer, Berlin, Heidelberg
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