Observability and uniqueness theorem for a coupled hyperbolic system
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. T...
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200002477 |
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| _version_ | 1832548685760692224 |
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| author | Boris V. Kapitonov Joel S. Souza |
| author_facet | Boris V. Kapitonov Joel S. Souza |
| author_sort | Boris V. Kapitonov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-87ef99a88cf241059943af26bf22203a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-87ef99a88cf241059943af26bf22203a2025-02-03T06:13:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0124642343210.1155/S0161171200002477Observability and uniqueness theorem for a coupled hyperbolic systemBoris V. Kapitonov0Joel S. Souza1Institute of Mathematics, Russian Academy of Sciences and Universidade Federal de Santa Catarina, RussiaDepartamento de Matemática da Universidade Federal de Santa Catarina C.P. 476, Florianópolis, SC CEP 88040-900, BrazilWe 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.http://dx.doi.org/10.1155/S0161171200002477Observabilityinverse inequalityuniqueness theoremunique continuation. |
| spellingShingle | Boris V. Kapitonov Joel S. Souza Observability and uniqueness theorem for a coupled hyperbolic system International Journal of Mathematics and Mathematical Sciences Observability inverse inequality uniqueness theorem unique continuation. |
| title | Observability and uniqueness theorem for a coupled hyperbolic system |
| title_full | Observability and uniqueness theorem for a coupled hyperbolic system |
| title_fullStr | Observability and uniqueness theorem for a coupled hyperbolic system |
| title_full_unstemmed | Observability and uniqueness theorem for a coupled hyperbolic system |
| title_short | Observability and uniqueness theorem for a coupled hyperbolic system |
| title_sort | observability and uniqueness theorem for a coupled hyperbolic system |
| topic | Observability inverse inequality uniqueness theorem unique continuation. |
| url | http://dx.doi.org/10.1155/S0161171200002477 |
| work_keys_str_mv | AT borisvkapitonov observabilityanduniquenesstheoremforacoupledhyperbolicsystem AT joelssouza observabilityanduniquenesstheoremforacoupledhyperbolicsystem |