We set a coupled boundary value problem between two domains of different dimension. The first one is the unit cube of Rn, n C [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.
@article{urn:eudml:doc:44315,
title = {Exact controllability of a pluridimensional coupled problem.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {5},
year = {1992},
pages = {91-135},
zbl = {0760.35012},
mrnumber = {MR1183428},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44315}
}
Nicaise, Serge. Exact controllability of a pluridimensional coupled problem.. Revista Matemática de la Universidad Complutense de Madrid, Tome 5 (1992) pp. 91-135. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44315/