We introduce a model of a vibrating multidimensional structure made of a n-dimensional body and a one-dimensional rod. We actually consider the anisotropic elastodynamic system in the n-dimensional body and the Euler-Bernouilli 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.
@article{urn:eudml:doc:41902,
title = {Stabilization of a coupled multidimensional system.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {19},
year = {2006},
pages = {277-296},
zbl = {1110.93045},
mrnumber = {MR2241432},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41902}
}
Nicaise, Serge; Sène, Abdoulaye. Stabilization of a coupled multidimensional system.. Revista Matemática de la Universidad Complutense de Madrid, Tome 19 (2006) pp. 277-296. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41902/