English
On the boundary control method
Post-edited
Auteurs : Oksanen, Lauri (Auteur de la Conférence)
CIRM (Editeur )
35L05 - Wave equation (hyperbolic PDE)
35L20 - Initial-boundary value problems for second-order hyperbolic equations
35R30 - Inverse problems for PDE
CIRM (Editeur )
Résumé :
This is a survey talk about the Boundary Control method. The method originates from the work by Belishev in 1987. He developed the method to solve the inverse boundary value problem for the acoustic wave equation with an isotropic sound speed. The method has proven to be very versatile and it has been applied to various inverse problems for hyperbolic partial differential equations. We review recent results based on the method and explain how a geometric version of method works in the case of the wave equation for the Laplace-Beltrami operator on a compact Riemannian manifold with boundary.
Codes MSC : 35L05 - Wave equation (hyperbolic PDE)
35L20 - Initial-boundary value problems for second-order hyperbolic equations
35R30 - Inverse problems for PDE
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 28/04/15 Date de captation : 14/04/15 Sous collection : Research School arXiv category : Analysis of PDEs Domaine : PDE Format : QuickTime (.mov) Durée : 00:58:10 Audience : Researchers Download : https://videos.cirm-math.fr/2015-04-14_Oksanen.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Summer pre-school on inverse problems / Ecole d'été sur les problèmes inversesOrganisateurs de la rencontre : Dos Santos Ferreira, David ; Guillarmou, Colin ; Lassas, Matti ; Le Rousseau, Jérôme Dates : 13/04/15 - 17/04/15 Année de la rencontre : 2015 URL Congrès : http://iecl.univ-lorraine.fr/~David.Dos-...
Données de citation
DOI : 10.24350/CIRM.V.18752103Citer cette vidéo: Oksanen, Lauri (2015). On the boundary control method. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18752103 URI : http://dx.doi.org/10.24350/CIRM.V.18752103 |
Bibliographie
- Liu, S., & Oksanen, L. (2012). A Lipschitz stable reconstruction formula for the inverse problem for the wave equation.
- Lassas, M., & Oksanen, L. (2014. Inverse problem for the Riemannian wave equation with Dirichlet data and Neumann data on disjoint sets. Duke Mathematical Journal, 163(6), 1071-1103 - http://dx.doi.org/10.1215/00127094-2649534
