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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 wave equation when the control is applied on a part of the boundary. Relationships between the geometry of the domain, the geometry of the controlled boundary, the time needed to control and the energy of the control are dealt with. A new norm of the control and an energetic cost factor are introduced. These quantities enable a detailed appraisal of the numerical solutions obtained and the detection of 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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