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Regularity of plate equations with control concentrated in interior curves

Published online by Cambridge University Press:  14 November 2011

Stéphane Jaffard  and
Marius Tucsnak
Stéphane Jaffard
Affiliation:
Centre de Mathématiques et de Leurs Applications (CMLA), ENS de Cachan, 61 Av. du Président Wilson, 94235 Cachanand Université Paris 12 Créteil, France
Marius Tucsnak
Affiliation:
Centre de Mathématiques Appliqués (CMAP), Ecole Polytechnique, 91128 Palaiseauand Université de Versailles, France
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Synopsis

We consider initial and boundary-value problems modelling the vibration of a plate with piezoelectric actuator. The usual models lead to the Bernoulli–Euler and Kirchhoff plate equations with right-hand side given by a distribution concentrated in an interior curve. We obtain regularity results which are stronger than those obtained by simply using the Sobolev regularity of the right-hand side. By duality, we obtain new trace regularity properties for the solutions of plate equations. Our results provide appropriate function spaces for the control of plates provided with piezoelectric actuators.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 5 , 1997 , pp. 1005 - 1025
Copyright
Copyright © Royal Society of Edinburgh 1997

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