Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients. (English) Zbl 1069.35035
Summary: One of the basic inverse problems in an anisotropic media is the determination of coefficients in a bounded domain with a single measurement. We consider the problem of finding the coefficient of the second derivatives in a second-order hyperbolic equation with variable coefficients.
Under a weak regularity assumption and a geometrical condition on the metric, we prove the uniqueness in a multidimensional hyperbolic inverse problem with a single measurement. Moreover we show that our uniqueness results yield the Lipschitz stability estimate in \(L^2\) space for the solution to the inverse problem under consideration.
Under a weak regularity assumption and a geometrical condition on the metric, we prove the uniqueness in a multidimensional hyperbolic inverse problem with a single measurement. Moreover we show that our uniqueness results yield the Lipschitz stability estimate in \(L^2\) space for the solution to the inverse problem under consideration.
MSC:
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 35R30 | Inverse problems for PDEs |
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