Simultaneous controllability in sharp time for two elastic strings
ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 259-273.

We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.

Classification : 93B, 35L, 42
Mots clés : exact controllability, spectral controllability, approximate controllability, simultaneous controllability, string equation, boundary control, Riesz basis 
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     title = {Simultaneous controllability in sharp time for two elastic strings},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {259--273},
     publisher = {EDP-Sciences},
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     url = {http://www.numdam.org/item/COCV_2001__6__259_0/}
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Avdonin, Sergei; Tucsnak, Marius. Simultaneous controllability in sharp time for two elastic strings. ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 259-273. http://www.numdam.org/item/COCV_2001__6__259_0/

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