Unicité et contrôle pour le système de Lamé
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 6, page 561-592
- ISSN: 1292-8119
Access Full Article
top
Abstract
topHow to cite
topBellassoued, Mourad. "Unicité et contrôle pour le système de Lamé." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 561-592. <http://eudml.org/doc/116577>.
@article{Bellassoued2010,
abstract = {
In this paper, we study the uniqueness problem for the Lamé
system. We prove that we have the uniqueness property across any
non characteristic surface. We also give two results which apply
to the boundary controllability for the Lamé system.
},
author = {Bellassoued, Mourad},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Uniqueness; controllability; elastic wave equation.; elastic wave equation; local Cauchy uniqueness; non-characteristic surface; Fourier transform; Carleman inequality; boundary control; Hilbert uniqueness approach of Lions},
language = {eng},
month = {3},
pages = {561-592},
publisher = {EDP Sciences},
title = {Unicité et contrôle pour le système de Lamé},
url = {http://eudml.org/doc/116577},
volume = {6},
year = {2010},
}
TY - JOUR
AU - Bellassoued, Mourad
TI - Unicité et contrôle pour le système de Lamé
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 6
SP - 561
EP - 592
AB -
In this paper, we study the uniqueness problem for the Lamé
system. We prove that we have the uniqueness property across any
non characteristic surface. We also give two results which apply
to the boundary controllability for the Lamé system.
LA - eng
KW - Uniqueness; controllability; elastic wave equation.; elastic wave equation; local Cauchy uniqueness; non-characteristic surface; Fourier transform; Carleman inequality; boundary control; Hilbert uniqueness approach of Lions
UR - http://eudml.org/doc/116577
ER -
References
top- S. Alinhac, Non unicité du problème de Cauchy. Ann. Math.117 (1983) 77-108.
- S. Alinhac et M.S. Baouendi, A non uniqueness result for operators of principal type. Math. Z.220 (1995) 561-568.
- D. Ang, M. Ikehata, D. Trong et M. Yamampto, Unique continuation for a stationary isotropic Lamé system with variable coefficients. Comm. Partial Differential Equations23 (1998) 371-385.
- B. Dehman et L. Robbiano, La propriété du prolongement unique pour un système elliptique. Le système de Lamé. J. Math. Pures Appl.72 (1993) 475-492.
- M. Eller, V. Isakov, G. Nakamura et D. Tataru, Uniqueness and Stability in the Cauchy Problem for Maxwell' and elasticity systems. Preprint.
- L. Hörmander, On the uniqueness of the Cauchy problem under partial analy-ticity assumptions. Preprint (1996).
- L. Hörmander, Linear partial differential operators. Springer Verlag, Berlin (1963).
- L. Hörmander, The analysis of linear partial differential operators, I-III. Springer Verlag.
- V. Isakov, A non hyperbolic Cauchy problem for and its applications to elasticity theory. Comm. Pure Math. Appl.39 (1986) 747-767.
- N. Lerner, Unicité de Cauchy pour des opérateurs faiblement principalement normaux. J. Math. Pures Appl.64 (1985) 1-11.
- J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation des systèmes distribués. Masson, Collection RMA, Paris (1988).
- L. Robbiano, Théorème d'unicité adapté au contrôle des solutions des problèmes hyperboliques. Comm. Partial Differential Equations16 (1991) 789-800.
- L. Robbiano et C. Zuily, Uniqueness in the Cauchy problem for operators with partially holomorphic coefficients. Invent. Math.131 (1998) 493-539.
- J. Sjöstrand, Singularités analytiques microlocales. Astérisque95 (1982).
- D. Tataru, Unique continuation for solutions to P.D.E's between Hörmander's theorem and Holmgren's theorem. Comm. on P.D.E.20 (1995) 855-884.
- C. Zuily, Lectures on uniqueness and non uniqueness in the Cauchy probem. Birkhäuser, Progress in Math.33 (1983).
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.