SIAM Journal on Applied Mathematics


SIAM J. Appl. Math., 62(1), 94–106. (13 pages)

Boundary Integral Formulae for the Reconstruction of Imperfections of Small Diameter in an Elastic Medium

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Article Data

History

Published online: 27 July 2006

AMS Subject Headings

73D50, 35R30, 35B30

Publication Data

ISSN (print): 0036-1399
ISSN (online): 1095-712X
Publisher: Society for Industrial and Applied Mathematics
CODEN: smjmap
Carlos Alves and Habib Ammari
https://doi.org/10.1137/S0036139900369266

We consider an isotropic Lamé system for an elastic medium consisting of finitely many imperfections of small diameter, embedded in a homogeneous reference medium. The Lamé coefficients of the imperfections are different from those of the background medium. First, we establish an asymptotic formula for the displacement vector in terms of the reference Lamé coefficients, the location of the imperfections, and their geometry. Second, we use this asymptotic expansion to establish continuous dependence estimates for certain characteristics of the imperfections in terms of the boundary data and to derive integral boundary formulae that yield to a very effective identification procedure.

Copyright © 2001 Society for Industrial and Applied Mathematics
Permalink: https://doi.org/10.1137/S0036139900369266

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