Выходит 12 номеров в год
ISSN Печать: 1064-2315
ISSN Онлайн: 2163-9337
Indexed in
On Determination of the Coefficient of Derivative in the Equation of a String Oscillations with Discontinuity
Краткое описание
The problem of determination of the coefficient for the right first order derivative in the equation of string oscillations is considered. The stated problem is reduced to the problem of optimal control. Theorem of existence of an optimal pair in the new problem, the Frechet differentiability of the constructed functional are proved, the necessary condition of optimality in the form of variational inequality is derived.
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Kabanikhin S.I., Iskakov K.T., Optimization methods for solving coefficient inverse problems [in Russian], NGU, Novosibirsk, 2001.
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Kabanikhin S.I., Inverse and ill-posed problems, 2-nd ed. [in Russian], Sibirskoe nauchnoye izdatelstvo, Novosibirsk, 2009.
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Anikonov Yu.E., Abasheyeva N.L., Ayupova N.B., Kozhanov A.I., Neshchadim M.V., Valitov I.R., Inverse problems for evolutionary equations, Sibirskiye electronnyye matematicheskiye izvestiya, 2008, 5, 549–580.
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Kabanikhin S.I., Shishlenin M.A., On the use of a priori information in the coefficient inverse problems for hyperbolic equations, Trudy IMM UrO RAN, 2012, 18, No. 1, 147–164.
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Romanov V.G., Some inverse problems for equations of hyperbolic type [in Russian], Nauka, Novosibirsk, 1972.
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Romanov V.G., One-dimensional inverse problem for wave equation, Doklady AN SSSR, 1973, 211, No. 5, 1083–1084.
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Lions J.L., Control of singular distributed systems [Russian translation], Nauka, Moscow, 1987.
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Ladyzhenskaya O.A., Boundary value problems of mathematical physics [in Russian], Nauka, Moscow, 1973.
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Lions J.L., Magenes E., Inhomogeneous boundary value problems and their applications [Russian translation], Mir, Moscow, 1971.