Hostname: page-component-7dd5485656-g8tfn Total loading time: 0 Render date: 2025-10-31T07:22:59.815Z Has data issue: false hasContentIssue false
  • English
  • Français

Unicité et contrôle pour le système de Lamé

Published online by Cambridge University Press:  15 August 2002

Mourad Bellassoued
Mourad Bellassoued*
Affiliation:
Faculté des Sciences de Bizerte, Département des Mathématiques, 7021 Jarzouna Bizerte, Tunisie ; mourad.bellassoued@fsb.rnu.tn.
Get access

Abstract

In this paper, we study the uniqueness problem for the Lamésystem. We prove that we have the uniqueness property across anynon characteristic surface. We also give two results which applyto the boundary controllability for the Lamé system.

Keywords

Uniquenesscontrollabilityelastic wave equation.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 561 - 592
Copyright
© EDP Sciences, SMAI, 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Alinhac, S., Non unicité du problème de Cauchy. Ann. Math. 117 (1983) 77-108. CrossRef
Alinhac, S. et Baouendi, M.S., A non uniqueness result for operators of principal type. Math. Z. 220 (1995) 561-568. CrossRef
Ang, D., Ikehata, M., Trong, D. et Yamampto, M., Unique continuation for a stationary isotropic Lamé system with variable coefficients. Comm. Partial Differential Equations 23 (1998) 371-385. CrossRef
Dehman, B. et Robbiano, L., 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.
Isakov, V., A non hyperbolic Cauchy problem for $\fbox{} _a.\fbox{} _b$ and its applications to elasticity theory. Comm. Pure Math. Appl. 39 (1986) 747-767. CrossRef
Lerner, N., 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).
Robbiano, L., Théorème d'unicité adapté au contrôle des solutions des problèmes hyperboliques. Comm. Partial Differential Equations 16 (1991) 789-800. CrossRef
Robbiano, L. et Zuily, C., Uniqueness in the Cauchy problem for operators with partially holomorphic coefficients. Invent. Math. 131 (1998) 493-539. CrossRef
J. Sjöstrand, Singularités analytiques microlocales. Astérisque 95 (1982).
Tataru, D., 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).