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AN INVERSE INITIAL BOUNDARY VALUE PROBLEM FOR THE WAVE EQUATION IN THE PRESENCE OF IMPERFECTIONS OF
 

Summary: AN INVERSE INITIAL BOUNDARY VALUE PROBLEM FOR THE
WAVE EQUATION IN THE PRESENCE OF IMPERFECTIONS OF
SMALL VOLUME
HABIB AMMARI
SIAM J. CONTROL OPTIM. c 2002 Society for Industrial and Applied Mathematics
Vol. 41, No. 4, pp. 1194­1211
Dedicated to Jean-Claude N´ed´elec for his 60th birthday
Abstract. We consider for the wave equation the inverse problem of identifying locations and
certain properties of the shapes of small conductivity inhomogeneities in a homogeneous background
medium from dynamic boundary measurements on part of the boundary and for a finite interval in
time. Using as weights particular background solutions constructed by a geometrical control method,
we develop an asymptotic method based on appropriate averaging of the partial dynamic boundary
measurements. Our approach is expected to lead to very effective computational identification algo-
rithms.
Key words. inverse problem, wave equation, reconstruction, geometric control
AMS subject classifications. 35R30, 35B40, 35B37, 35L05
PII. S0363012901384247
1. The inverse initial boundary value problem. Let be a bounded,
smooth subdomain of R2
. For simplicity, we take to be C

  

Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique

 

Collections: Mathematics