Comptes Rendus
Partial differential equations/Optimal control
Source identification for the wave equation on graphs
Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 907-912.

We consider source identification problems for the wave equation on an interval and on trees. The main advantage of our approach is its locality. Our algorithm reduces essentially to the resolution of a linear integral Volterra equation of the second kind and is new even for an interval.

Nous considérons un problème d'identification de sources pour l'équation des ondes sur un intervalle ou sur des arbres. L'avantage principal de notre approche est sa localité. Notre algorithme se réduit essentiellement à la résolution d'une équation intégrale de Volterra du second ordre et est nouveau, même pour un intervalle.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.09.008
Sergei Avdonin 1; Serge Nicaise 2

1 Dept. of Mathematics and Statistics, University of Alaska, Fairbanks, AK 99775, USA
2 Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, 59313 Valenciennes cedex 9, France
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Sergei Avdonin; Serge Nicaise. Source identification for the wave equation on graphs. Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 907-912. doi : 10.1016/j.crma.2014.09.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.008/

[1] S. Avdonin; S. Nicaise Source identification for the wave equation on graphs, Lamav, Université de Valenciennes, France, 2014 (Technical report in preparation)

[2] G. Bruckner; M. Yamamoto On the determination of point sources by boundary observations: uniqueness, stability and reconstruction, WIAS, Berlin, 1996 (Technical report 252)

[3] S. Nicaise; O. Zair Identifiability, stability and reconstruction results of point sources by boundary measurements in heterogeneous trees, Rev. Mat. Complut., Volume 16 (2003), pp. 151-178

[4] M. Yamamoto Well-posedness of an inverse hyperbolic problem by the Hilbert uniqueness method, J. Inverse Ill-Posed Probl., Volume 2 (1994) no. 4, pp. 349-368

[5] M. Yamamoto Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method, Inverse Probl., Volume 11 (1995) no. 2, pp. 481-496

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