Recherche et téléchargement d’archives de revues mathématiques numérisées

  
 
  Table des matières de ce fascicule | Article précédent | Article suivant
Imanuvilov, Oleg Yu.; Yamamoto, Masahiro
Remarks on Carleman estimates and exact controllability of the Lamé system. Journées équations aux dérivées partielles (2002), Art. No. 5, 19 p.
Texte intégral djvu | pdf | Analyses MR 1968201 | 1 citation dans Numdam

URL stable: http://www.numdam.org/item?id=JEDP_2002____A5_0

Résumé

In this paper we established the Carleman estimate for the two dimensional Lamé system with the zero Dirichlet boundary conditions. Using this estimate we proved the exact controllability result for the Lamé system with with a control locally distributed over a subdomain which satisfies to a certain type of nontrapping conditions.

Bibliographie

[AK1] F. Alabau, V. Komornik. Boundary observability and controllability of linear elastodynamic systems, Optimization methods in partial differential equations, AMS, Providence (1997). V-17  Zbl 0889.35060
[AK2] F. Alabau, V. Komornik. Boundary observability, controllability and stabilization of linear elastodynamic systems, SIAM J. Control Optimization 37, 521-542.  MR 1665070 |  Zbl 0935.93037
[AITY] D. Ang, M. Ikehata, D. Trong and M. Yamamoto. Unique continuation for a stationary isotropic Lamé system, Com. P.D.E 21, 371-385 (1998).  MR 1608540 |  Zbl 0892.35054
[B1] M. Bellassoued. Distribution of resonances and decay of the local energy for the elastic wave equations, Comm. Math. Phys. 215, 375-408 (2000).  MR 1799852 |  Zbl 0978.35077
[B2] M. Bellassoued. Carleman estimates and Decay Rate of the local energy for the Neumann problem of elasticity, Progr. Nonlinear Differential Equations Appl. 46,15-36 (2001).  MR 1839164 |  Zbl 0983.35031
[B3] M. Bellassoued. Unicité et contrôlle pour le système de Lamé, ESIAM 6, 561-592 (2001).
Numdam |  MR 1872389 |  Zbl 1007.35006
[DR] B. Dehman and L. Robbiano. La propriété du prolongement unique pour un systeme elliptique le système de Lamé, J. Math. Pure Appl. 72, 475-492 (1993).  MR 1239100 |  Zbl 0832.73012
[E1] Y. Egorov. Linear differential equations of the principal type, Consultants Bureau, New York (1986).  MR 872855 |  Zbl 0669.35001
[E2] Y. Egorov. The uniqueness of the solutions of the Cauchy Problem, Dokl. Akad. Nauk. SSSR 264 (4), 812-814 (1982).  MR 659579 |  Zbl 0509.35002
[EINT] M. Eller, V. Isakov, G. Nakamura and D. Tataru. Uniqueness and stability in the Cauchy problem for Maxwell's and the elasticity system, Nonlinear Partial Differential Equations, Vol. 16, Collège de France Seminar, ElsevierGauthier Villars "Series in Applied Mathematics", Ed. P.G. Ciarlet, P.L. Lions 7, (2002).  MR 1936000 |  Zbl 1038.35159
[Hö] L. Hörmander L. Partial Differential Operators, Springer-Verlag, Berlin (1963).
[H] M.A. Horn. Implications of sharp regularity results on boundary stabilization of the system of linear elastisity, J. Math. Analysis and Applications 223, 126-150 (1998).  MR 1627344 |  Zbl 0913.93062
[Im] O. Imanuvilov. On Carleman estimates for hyperbolic equations, to appear in Asymptotic Analysis.  MR 1993649 |  Zbl 1050.35046
[IIY] O. Imanuvilov, V. Isakov, M. Yamamoto. An inverse problem for the dynamical Lamé system with two sets of boundary data, Preprint (2002).  MR 1980857
[La] J. Lagnese. Boundary stabilization of Thin Plates, SIAM studies in Applied Mathematics (1989).  MR 1061153 |  Zbl 0696.73034
[LL] J. Lagnese and J.L. Lions. Modeling, Analysis and Control of the thin plates, Masson, Paris (1988). V-18  MR 953313 |  Zbl 0662.73039
[Li] J.L. Lions. Contrôlabilité exacte, perturbation et stabilization de systèmes distribués, Vol 1, Masson, Paris, 1988.  Zbl 0653.93002
[NW] G. Nakamura, J.-N. Wang. Unique continuation and the Runge approximation property for anisotropic elasticity, Preprint.
[T1] M. Taylor. Pseudodifferential operators, Princeton University Press, Princeton, New Jersey (1981).  MR 618463 |  Zbl 0453.47026
[T2] M. Taylor. Pseudodifferential Operators and Nonlinear PDE, Birkhäuser, Boston Basel Berlin (1991).  MR 1121019 |  Zbl 0746.35062
[Y1] K. Yamamoto. Singularities of solutions to the boundary value problems for elastic and Maxwell's equation, Japan J. Math. 14 (1),119-163 (1988).  MR 945621 |  Zbl 0669.73017
[Y2] K. Yamamoto. Exponential energy decay of solutions of elastic wave equations with the Dirichlet condition, Math. Scand. 65, 2006-220 (1989).  MR 1050865 |  Zbl 0757.73013
[Zui] C. Zuily. Uniqueness and non-uniqueness in Cauchy problem, Birkhäuser, Boston Basel Berlin (1983).  MR 701544 |  Zbl 0521.35003
[W1] N. Weck. Aussenraumaufgaben in der Theorie stationärer Schwingungen inhomogener elastischer Körper, Math. Z. 111, 387-398 (1969).
Article |  MR 263295 |  Zbl 0176.09202
[W2] N. Weck. Unique continuation for systems with Lamé principal part, Math. Meth. Appl. Sci. 24, 595-605 (2001)  MR 1834916 |  Zbl 0986.35117
Copyright Cellule MathDoc 2013 | Crédit | Plan du site