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Exact boundary controllability for the wave equation in domains with small holes. (English) Zbl 0843.35009
The authors consider the wave equation with Dirichlet boundary controls in perforated domains with small holes. Their aim is to give an answer to a uniform exact controllability time not depending on the perturbations. Weighted controls are supplied to the whole boundary which allow to describe the asymptotic behavior of the system. When the size of the holes is small enough, at the limit the wave equation is achieved with a boundary control. When the holes are of critical size, the wave equation is obtained, at the limit, with an additional term of order zero and two controls: the first one is a boundary control and the second one an internal control.

35B37 PDE in connection with control problems (MSC2000)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations