Comptes Rendus
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

Sergei Avdonin1 ; Serge Nicaise2
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, Volume 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

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 
@article{CRMATH_2014__352_11_907_0,
     author = {Sergei Avdonin and Serge Nicaise},
     title = {Source identification for the wave equation on graphs},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {907--912},
     publisher = {Elsevier},
     volume = {352},
     number = {11},
     year = {2014},
     doi = {10.1016/j.crma.2014.09.008},
     language = {en},
}
TY  - JOUR
AU  - Sergei Avdonin
AU  - Serge Nicaise
TI  - Source identification for the wave equation on graphs
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 907
EP  - 912
VL  - 352
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crma.2014.09.008
LA  - en
ID  - CRMATH_2014__352_11_907_0
ER  - 
%0 Journal Article
%A Sergei Avdonin
%A Serge Nicaise
%T Source identification for the wave equation on graphs
%J Comptes Rendus. Mathématique
%D 2014
%P 907-912
%V 352
%N 11
%I Elsevier
%R 10.1016/j.crma.2014.09.008
%G en
%F CRMATH_2014__352_11_907_0
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

  • Emilia Blåsten; Hiroshi Isozaki; Matti Lassas; Jinpeng Lu Inverse Problems for Discrete Heat Equations and Random Walks for a Class of Graphs, SIAM Journal on Discrete Mathematics, Volume 37 (2023) no. 2, p. 831 | DOI:10.1137/21m1439936
  • Amin Boumenir; Vu Kim Tuan The reconstruction of a wave equation from one side measurement, Wave Motion, Volume 95 (2020), p. 102547 | DOI:10.1016/j.wavemoti.2020.102547
  • S. A. Avdonin; G. Y. Murzabekova; K. B. Nurtazina Source Identification for the Differential Equation with Memory, New Trends in Analysis and Interdisciplinary Applications (2017), p. 111 | DOI:10.1007/978-3-319-48812-7_15
  • Sergei Avdonin; Serge Nicaise Source identification problems for the wave equation on graphs, Inverse Problems, Volume 31 (2015) no. 9, p. 095007 | DOI:10.1088/0266-5611/31/9/095007

Cité par 4 documents. Sources : Crossref

Commentaires - Politique