Full paper in PDF:
$%S. Nicaise and O. Zaïr, Identifiability, stability, and reconstruction results of point sources by boundary measurements in heteregeneous trees, Rev. Mat. Complut. 16 (2003), 151–178.%$

Identifiability, Stability, and Reconstruction Results of Point Sources by Boundary Measurements in Heterogeneous Trees

Serge NICAISE and Ouahiba ZAïR
Université de Valenciennes et du Hainaut Cambrésis
MACS, ISTV
F-59313 - Valenciennes Cedex 9 — France
snicaise@univ-valenciennes.fr
Université des Sciences et de la Technologie H. Boumediene

Institut de Mathématiques
El-Alia, B.P. 32
Bab Ezzouar, Alger — Algeria

Received: March 4, 2002
Accepted: July 8, 2002
ABSTRACT

We consider the inverse problem of determining point wave sources in heterogeneous trees, extensions of one-dimensional stratified sets. We show that the Neumann boundary observation on a part of the lateral boundary determines uniquely the point sources if the time of observation is large enough. We further establish a conditional stability and give a reconstructing scheme.

Key words: inverse problem.
2000 Mathematics Subject Classification: 35R30, 35J25.