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Stabilization of a coupled multidimensional system. (English) Zbl 1110.93045
Summary: We introduce a model of a vibrating multidimensional structure made of an \(n\)-dimensional body and a one-dimensional rod. We actually consider the anisotropic elastodynamic system in the \(n\)-dimensional body and the Euler-Bernoulli beam in the one-dimensional rod. These equations are coupled via their boundaries. Using appropriate feedbacks on a part of the boundary we show the exponential decay of the energy of the system.
MSC:
93D15 Stabilization of systems by feedback
93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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