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Exact controllability of vibrations of thin bodies. (English) Zbl 0809.93025

Summary: We address the problem of exact controllability of the wave equation in three dimensional domains which are thin in one direction. We prove the existence of exact controls and analyze their asymptotic behaviour as thickness parameter goes to zero. We characterize their limit as the solution of an exact controllability problem in two dimension.

MSC:

93C20 Control/observation systems governed by partial differential equations
93B05 Controllability
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
74J10 Bulk waves in solid mechanics
74J99 Waves in solid mechanics
74K20 Plates
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