International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 6, Pages 423-432
doi:10.1155/S0161171200002477
Observability and uniqueness theorem for a coupled hyperbolic system
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.
Abstract
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.