 
Summary: ESAIM: Control, Optimisation and Calculus of Variations
URL: http://www.emath.fr/cocv/
May 1998, Vol. 3, 163{212
GEOMETRICAL ASPECTS OF EXACT BOUNDARY
CONTROLLABILITY FOR THE WAVE EQUATION {
A NUMERICAL STUDY
M. ASCH AND G. LEBEAU
Abstract. This essentially numerical study, sets out to investigate vari
ous geometrical properties of exact boundary controllability of the wave
equation when the control is applied on a part of the boundary. Re
lationships 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.
Contents
1. Introduction 164
2. The HUM approach to exact boundary controllability 165
2.1. Formulation of the problem 165
2.2. Description of the HUM 165
