Observability of rectangular membranes and plates on small sets

Vilmos Komornik; Paola Loreti

doi:10.3934/eect.2014.3.287

Article Contents

2014, Volume 3, Issue 2: 287-304. Doi: 10.3934/eect.2014.3.287

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Observability of rectangular membranes and plates on small sets

Vilmos Komornik^1, and
Paola Loreti^2,

1.
Département de mathématique, Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg Cedex
2.
Sapienza Università di Roma, Sapienza Università di Roma, Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sezione Matematica, Via A. Scarpa n.16 00161 Roma

Received: October 31, 2013

Revised: March 31, 2014

Published: May 2014

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Abstract

Since the works of Haraux and Jaffard we know that rectangular plates may be observed by subregions not satisfying the geometrical control condition. We improve these results by observing only on an arbitrarily short segment inside the domain. The estimates may be strengthened by observing on several well-chosen segments.
In the second part of the paper we establish various observability theorems for rectangular membranes by applying Mehrenberger's recent generalization of Ingham's theorem.

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Mathematics Subject Classification: 42C99, 93B07.

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References

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