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Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin, Marius Tucsnak (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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.

Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin, Marius Tucsnak (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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.

Small vertical vibrations of strings with moving ends.

Tania Nunes Rabello, María Cristina Campos Vieira, Cicero Lopes Frota, Luis Adauto Medeiros (2003)

Revista Matemática Complutense

In this work we investigate a mathematical model for small vertical vibrations of a stretched string when the ends vary with the time t and the cross sections of the string is variable and the density of the material is also variable, that is, p=p(x). It contains Kirchhoff model for fixed ends. We obtain solutions by Galerkin method and estimates in Sobolev spaces.

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