no. 11
Partial differential equations/Optimal control
Source identification for the wave equation on graphs
[Identification de sources pour l'équation des ondes sur des graphes]

Présenté par : Gilles Lebeau

Avdonin, Sergei1 ; Nicaise, Serge2
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
Comptes Rendus. Mathématique, Tome 352 (2014) no. 11, pp. 907-912.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.09.008
Avdonin, Sergei 1 ; Nicaise, Serge 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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Avdonin, Sergei; Nicaise, Serge. Source identification for the wave equation on graphs. Comptes Rendus. Mathématique, Tome 352 (2014) no. 11, pp. 907-912. doi : 10.1016/j.crma.2014.09.008. http://www.numdam.org/articles/10.1016/j.crma.2014.09.008/

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

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

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

[4] Yamamoto, M. 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] Yamamoto, M. 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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