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Sibirskii Matematicheskii Zhurnal, 2002, Volume 43, Number 3, Pages 702–709
(Mi smj1323)
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A stability estimate for a solution in the inverse problem of finding the coefficients of lower derivatives
V. G. Romanov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
We consider the problem of finding the coefficients of the first derivatives in a second-order hyperbolic equation. The additional information is the trace of a solution and its normal derivative on the lateral surface of the cylindrical domain of some direct problem for the original equation. The impulse point source lies outside the domain in which the sought coefficients are determined and is a parameter of the problem. We suppose that the number of sources for which the trace of a solution is given coincides with the number of the coefficients to be determined. The main result of this article is a stability estimate for a solution to the inverse problem under consideration.
Received: 16.01.2002
Citation:
V. G. Romanov, “A stability estimate for a solution in the inverse problem of finding the coefficients of lower derivatives”, Sibirsk. Mat. Zh., 43:3 (2002), 702–709; Siberian Math. J., 43:3 (2002), 568–574
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https://www.mathnet.ru/eng/smj1323 https://www.mathnet.ru/eng/smj/v43/i3/p702
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