×

Boundary determintion for an inverse problem in elastodynamics. (English) Zbl 0982.35122

The author considers the problem of uniquely determining material properties (density and elasticity) of a three-dimensional bounded, inhomogeneous isotropic elastic body from measurements, made on the surface, of displacements resulting from forces applied on the surface. Modeling surface measurements by the Dirichlet-to-Neumann map on a finite time interval, it is shown that the Dirichlet-to-Neumann map uniquely determines the density and elastic properties of the surface of the body. It is pointed out that in a subsequent paper by the author [An inverse problem in elastodynamics: uniqueness of the wave speeds in the interior, J. Differ. Equations l62, No. 2, 300-325 (2000; Zbl 0968.74040)] the result is applied to show that certain associated wave speeds are uniquely determined in the interior of the medium.

MSC:

35R30 Inverse problems for PDEs
74J25 Inverse problems for waves in solid mechanics
86A22 Inverse problems in geophysics

Citations:

Zbl 0968.74040
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1007/BF02390497 · Zbl 0503.58031 · doi:10.1007/BF02390497
[2] Duvaut G, Inequalities in mechanics and physics (1976) · doi:10.1007/978-3-642-66165-5
[3] Grigis A, London Math. Soc. Lecture Notes Series 196
[4] Hörmander, L. 1994. ”The Analysis of Linear Partial Differential Operators III”. Berlin: Springer-Verlag.
[5] DOI: 10.1007/BF00251584 · Zbl 0361.35046 · doi:10.1007/BF00251584
[6] DOI: 10.1121/1.1907775 · doi:10.1121/1.1907775
[7] DOI: 10.1002/cpa.3160370302 · Zbl 0586.35089 · doi:10.1002/cpa.3160370302
[8] Kupradze,ed, V.D. 1979. ”Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity”. Amsterdm: North Holland.
[9] DOI: 10.1002/cpa.3160130310 · Zbl 0098.29601 · doi:10.1002/cpa.3160130310
[10] DOI: 10.1215/S0012-7094-57-02471-7 · Zbl 0083.31801 · doi:10.1215/S0012-7094-57-02471-7
[11] DOI: 10.2307/2118653 · Zbl 0857.35135 · doi:10.2307/2118653
[12] DOI: 10.2307/2375069 · Zbl 0803.35164 · doi:10.2307/2375069
[13] DOI: 10.1007/BF01231541 · Zbl 0814.35147 · doi:10.1007/BF01231541
[14] DOI: 10.1006/jdeq.1999.3657 · Zbl 0968.74040 · doi:10.1006/jdeq.1999.3657
[15] DOI: 10.1007/BF02096553 · Zbl 0778.35060 · doi:10.1007/BF02096553
[16] DOI: 10.2307/1971291 · Zbl 0625.35078 · doi:10.2307/1971291
[17] DOI: 10.1002/cpa.3160410205 · Zbl 0632.35074 · doi:10.1002/cpa.3160410205
[18] Sylverster J, Contemporary Mathematics 122 pp 105– (1991) · doi:10.1090/conm/122/1135861
[19] Uhlmann G, Methods semi-classiques 207 pp 153– (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.