Exact controllability of a pluridimensional coupled problem.

Serge Nicaise

Revista Matemática de la Universidad Complutense de Madrid (1992)

  • Volume: 5, Issue: 1, page 91-135
  • ISSN: 1139-1138

Abstract

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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.

How to cite

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Nicaise, Serge. "Exact controllability of a pluridimensional coupled problem.." Revista Matemática de la Universidad Complutense de Madrid 5.1 (1992): 91-135. <http://eudml.org/doc/44315>.

@article{Nicaise1992,
abstract = {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.},
author = {Nicaise, Serge},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Ecuaciones diferenciales elípticas; Problemas de valor de frontera; Proceso controlable; mixed boundary-value problem; Hilbert space techniques},
language = {eng},
number = {1},
pages = {91-135},
title = {Exact controllability of a pluridimensional coupled problem.},
url = {http://eudml.org/doc/44315},
volume = {5},
year = {1992},
}

TY - JOUR
AU - Nicaise, Serge
TI - Exact controllability of a pluridimensional coupled problem.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1992
VL - 5
IS - 1
SP - 91
EP - 135
AB - 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.
LA - eng
KW - Ecuaciones diferenciales elípticas; Problemas de valor de frontera; Proceso controlable; mixed boundary-value problem; Hilbert space techniques
UR - http://eudml.org/doc/44315
ER -

Citations in EuDML Documents

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  1. Serge Nicaise, About the Lamé system in a polygonal or a polyhedral domain and a coupled problem between the Lamé system and the plate equation. II : exact controllability
  2. Serge Nicaise, About the Lamé system in a polygonal or a polyhedral domain and a coupled problem between the Lamé system and the plate equation. I : regularity of the solutions
  3. Bertrand Dekoninck, Serge Nicaise, Control of networks of Euler-Bernoulli beams
  4. Bertrand Dekoninck, Serge Nicaise, Control of networks of Euler-Bernoulli beams

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