Exact controllability of vibrations of thin bodies.
Saint Jean Paulin, Jeannine, Vanninathan, M. (1994)
Portugaliae Mathematica
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Saint Jean Paulin, Jeannine, Vanninathan, M. (1994)
Portugaliae Mathematica
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Lionel Rosier (1997)
ESAIM: Control, Optimisation and Calculus of Variations
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K. Beauchard, E. Zuazua (2009)
Annales de l'I.H.P. Analyse non linéaire
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Weijiu Liu (1998)
ESAIM: Control, Optimisation and Calculus of Variations
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Jean-Michel Coron (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.
T. Horsin (1998)
ESAIM: Control, Optimisation and Calculus of Variations
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Farid Ammar Khodja, Assia Benabdallah, Cédric Dupaix, Ilya Kostin (2005)
ESAIM: Control, Optimisation and Calculus of Variations
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We study the null controllability by one control force of some linear systems of parabolic type. We give sufficient conditions for the null controllability property to be true and, in an abstract setting, we prove that it is not always possible to control.