## Contrôle interne exact des vibrations d’une plaque rectangulaire. (Internal exact control for the vibrations of a rectangular plate).(French)Zbl 0718.49026

Consider the equation $$(\partial^ 2u/\partial t^ 2)+\Delta^ 2u=h(x,t)$$ of the control of a vibrating plate of rectangular shape with Dirichlet boundary conditions on u and $$\Delta$$ u. It is proved in this paper that any initial data $$(u,\partial u/\partial t)_{t=0}$$ belonging to $$(H^ 2\cap H^ 1_ 0)\times L^ 2$$ can be driven to rest in an arbitrarily small time by a control h(x,t) in $$L^ 2$$ supported by an arbitrarily small open subset of the rectangle. This result is derived from classical estimates on lacunary Fourier series.
Reviewer: S.Jaffard

### MSC:

 49N10 Linear-quadratic optimal control problems 35K25 Higher-order parabolic equations 93B05 Controllability 74H45 Vibrations in dynamical problems in solid mechanics
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