Appl Math Optim 54:223–235 (2006)
2006 Springer Science+Business Media, Inc.
Reconstruction of Elastic Inclusions of Small Volume
via Dynamic Measurements
and Hyeonbae Kang
Centre de Math´ematiques Appliqu´ees, Ecole Polytechnique,
91128 Palaiseau Cedex, France
School of Mathematical Sciences, Seoul National University,
Seoul 151-747, Korea
Abstract. We consider the inverse problem of identifying locations and certain
properties of the shapes of small elastic inclusions in a homogeneous background
medium from dynamic boundary measurements for a ﬁnite interval in time. Using
particular background solutions as weights, we present an asymptotic method based
on appropriate averaging of the dynamic boundary measurements and propose non-
iterative algorithms for solving our inverse problem.
Key Words. Elastic inclusions, Asymptotic expansions, Elastic moment tensors,
AMS Classiﬁcation. 35B30.
We suppose that the elastic medium occupies a bounded domain in R
, d = 2, 3, with
a connected C
-boundary ∂. Let the constants (λ
) denote the background Lam´e
coefﬁcients, that are the elastic parameters in the absence of any inclusion. Suppose that
The ﬁrst author was partly supported by ACI Nouvelles Interfaces des Math´ematiques No. 171 from
the Ministry of Education and Scientiﬁc Research, France. The second author was partly supported by KOSEF
98-0701-03-5 and BK21 at the School of Mathematical Sciences of SNU.