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Uniqueness in an inverse problem for an elasticity system. (Russian, English) Zbl 1050.35135

Sib. Mat. Zh. 45, No. 4, 747-757 (2004); translation in Sib. Math. J. 45, No. 4, 618-627 (2004).
The authors consider an inverse problem for a stationary elasticity system with constant Lamé coefficients and a variable matrix coefficient depending on the spatial variables and frequency. The right-hand side contains a delta-function whose support (source) varies in some domain disjoint from the support of the variable coefficient. The inverse problem is to find the coefficient from the scattered wave measured at the same point at which the perturbation originates. A uniqueness theorem is proven. The proof bases on reduction of the inverse problem to a family of equations with Riesz potential.

MSC:

35R30 Inverse problems for PDEs
74J25 Inverse problems for waves in solid mechanics
45K05 Integro-partial differential equations
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