Uniqueness of the density in an inverse problem for isotropic elastodynamics
Author:
Lizabeth V. Rachele
Journal:
Trans. Amer. Math. Soc. 355 (2003), 47814806
MSC (2000):
Primary 35R30
Published electronically:
July 28, 2003
MathSciNet review:
1997584
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Abstract: We consider the unique determination of the density of a nonhomogeneous, isotropic elastic object from measurements made at the surface. We model the behavior of the bounded, 3dimensional object by the linear, hyperbolic system of operators for isotropic elastodynamics. The material properties of the object (its density and elastic properties) correspond to the smooth coefficients of these differential operators. The data for this inverse problem, in the form of the correspondence between applied surface tractions and resulting surface displacements, is modeled by the dynamic DirichlettoNeumann map on a finite time interval. In an earlier paper we show that the speeds of (compressional and sheer) wave propagation through the object are uniquely determined by the DirichlettoNeumann map. Here we extend that result by showing that the density is also determined in the interior by the DirichlettoNeumann map in the case, for example, that at only isolated points in the object. We use techniques from microlocal analysis and integral geometry to solve this fully threedimensional problem.
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Additional Information
Lizabeth V. Rachele
Affiliation:
Department of Mathematics, Tufts University, Medford, Massachusetts 02155
Address at time of publication:
Department of Mathematics and Statistics, University at Albany, SUNY, Albany, New York 12222
Email:
lrachele@math.albany.edu
DOI:
http://dx.doi.org/10.1090/S0002994703032689
PII:
S 00029947(03)032689
Received by editor(s):
June 11, 2001
Published electronically:
July 28, 2003
Additional Notes:
The author was partially supported by U.S. National Science Foundation grant 9801664 (9996350)
Article copyright:
© Copyright 2003 American Mathematical Society
