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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 4, Pages 3–20
(Mi sjim800)
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This article is cited in 1 scientific paper (total in 1 paper)
An inverse problem of location type for a hyperbolic system
D. S. Anikonov, S. G. Kazantsev, D. S. Konovalova Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
Abstract:
We consider an inverse problem for a hyperbolic system of two first-order partial differential equations with two independent variables. The right-hand sides of the system are assumed discontinuous functions. The inverse problem consists in the determination of a certain hull which contains the discontinuity line of the right-hand sides. We first study the corresponding direct problem. The existence and uniqueness of a generalized solution to the direct problem are established, and the differential properties of this solution are studied. In particular, we prove that its first-order partial derivatives are unbounded near some rays directed along characteristics. This property is the base of the algorithm for solving the inverse problem. The inverse problem is considered in the two versions: in the first version the coefficients of the equations are given, and in the second, they are unknown.
Keywords:
inverse problem, hyperbolic equation, discontinuous function, generalized solution, differential property.
Received: 13.05.2013
Citation:
D. S. Anikonov, S. G. Kazantsev, D. S. Konovalova, “An inverse problem of location type for a hyperbolic system”, Sib. Zh. Ind. Mat., 16:4 (2013), 3–20
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https://www.mathnet.ru/eng/sjim800 https://www.mathnet.ru/eng/sjim/v16/i4/p3
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Abstract page: | 418 | Full-text PDF : | 117 | References: | 89 | First page: | 11 |
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