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Geometrical aspects of exact boundary controllability for the wave equation - anumerical study

Published online by Cambridge University Press:  15 August 2002

M. Asch  and
G. Lebeau
M. Asch
Affiliation:
(Mark.Asch@math.u-psud.fr) 
G. Lebeau
Affiliation:
(Gilles.Lebeau@math.polytechnique.fr)
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Abstract

This essentially numerical study, sets out to investigate various geometrical properties of exact boundary controllability of the waveequation when the control is applied on a part of the boundary. Relationships between the geometry of the domain, the geometry ofthe controlled boundary, the time needed to control and the energy of the control are dealt with. A new norm of the control and anenergetic cost factor are introduced. These quantities enable a detailed appraisal of the numerical solutions obtained and the detectionof trapped rays.

Keywords

Exact controllabilitygeometric opticswave equationfinite differences.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 3 , 1998 , pp. 163 - 212
Copyright
© EDP Sciences, SMAI, 1998

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