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H 2 On the boundary control method

Auteurs : Oksanen, Lauri (Auteur de la Conférence)
CIRM (Editeur )

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inverse boundary value problem hyperbolic systems/uniqueness results non-symmetric inverse problems billiard conditions computational implementations conformally product geometries Boundary Control method finite speed of propagation hyperbolic unique continuation Blagovescenskii's identity boundary distance functions cut locus volumes of domains of influence regularized control problem

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
35L20 - Initial-boundary value problems for second-order hyperbolic equations
35R30 - Inverse problems

Informations sur la rencontre

Nom du congrès : Summer pre-school on inverse problems / Ecole d'été sur les problèmes inverses
Organisteurs Congrès : 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-...

Citation Data

DOI : 10.24350/CIRM.V.18752103
Cite this video as: 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

  1. [1] Liu, S., & Oksanen, L. (2012). A Lipschitz stable reconstruction formula for the inverse problem for the wave equation. - http://arxiv.org/abs/1210.1094

  2. [2] 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



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