International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 6, Pages 423-432

Observability and uniqueness theorem for a coupled hyperbolic system

Boris V. Kapitonov1 and Joel S. Souza2

1Institute of Mathematics, Russian Academy of Sciences and Universidade Federal de Santa Catarina, Russia
2Departamento de Matemática da Universidade Federal de Santa Catarina C.P. 476, Florianópolis CEP 88040-900, SC, Brazil

Received 23 December 1998

Copyright © 2000 Boris V. Kapitonov and Joel S. Souza. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We deal with the inverse inequality for a coupled hyperbolic system with dissipation. The inverse inequality is an indispensable inequality that appears in the Hilbert Uniqueness Method (HUM), to establish equivalence of norms which guarantees uniqueness and boundary exact controllability results. The term observability is due to the mathematician Ho (1986) who used it in his works relating it to the inverse inequality. We obtain the inverse inequality by the Lagrange multiplier method under certain conditions.