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$%S. Nicaise, Exact controllability of a pluridimensional coupled problem, Rev. Mat. Univ. Complut. Madrid 5 (1992), no. 1, 91–135.%$

Exact Controllability of a Pluridimensional Coupled Problem

Serge NICAISE
Université de Sciences et Techniques de Lille Flandres Artois
U.F.R. de Mathématiques Pures et Appliquées
U.R.A.C.N.R.S. 751 F-59655 Villeneuve d’Ascq Cedex — France

Received: February 14, 1991
Revised: April 2, 1991
ABSTRACT

We set a coupled boundary value problem between two domains of different dimension. The first one is the unit cube of Rn , n (- [2,3] , with a crack and the second one is the crack. this problem comes from Ciarlet et al. (1989), that obtained an analogous coupled problem. We show that the solution has singularities due to the crack. As in Grisvard (1989), we adapt the Hilbert uniqueness method of J.-L. Lions (1968,1988) in order to obtain the exact controllability of the associated wave equation with Dirichlet action on a part of the boundary.

1991 Mathematics Subject Classification: 35C20, 49A22, 49E15.