Determination of a coefficient in the wave equation with a single measurement. (English) Zbl 1149.35404
Summary: We consider an inverse problem of finding the coefficient of the second-order 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 of Neumann data on a suitable sub-boundary. Moreover we show that our uniqueness yields the Lipschitz stability estimate in \(L^{2}\) space for solution to the inverse problem. The key is a Carleman estimate for a hyperbolic operator with variable coefficients.
MSC:
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 78A25 | Electromagnetic theory (general) |
| 35R30 | Inverse problems for PDEs |
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