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Journal of Automation and Information Sciences
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN Imprimer: 1064-2315
ISSN En ligne: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v51.i1.80
pages 78-85

On Determination of the Coefficient of the Lower Term of the Multidimensional Hyperbolic Equation of the Second Order

Gyunay Gafil kyzy Ismayilova
Sumgait State University, Sumgait (Azerbaijan)


Determination of the coefficient of the lower term of the multidimensional hyperbolic equation of the second order with the integral overdetermination condition is reduced to a problem of optimal control and the obtained problem is studied by methods of the theory of optimal control. A theorem about the existence of the optimal control is proved, continuous Frechet differentiability of the functional is ascertained and by means of solving the conjugate problem the necessary condition of optimality is derived.


  1. Kuliev G.F., Problem of optimal control of coefficients for equations of hyperbolic type, Izvestiya vuzov. Matematika, 1985, No. 3, 39–44.

  2. Kabanikhin S.I., Inverse and ill-posed problems, 2-nd ed. [in Russian], Novosibirsk, 2009.

  3. Kabanikhin S.I., Shishlenin M.A., Krivorotko O.I., Optimizational method of solving the inverse problem of thermal acoustics, Sibirskie elektronnyye matematicheskiye izvestiya, 2011, 263–292.

  4. Kabanikhin S.I., Shishlenin M.A., On the use of a priori information in the coefficient inverse problems for hyperbolic equations, Trudy IMM Ur ORAN, 2012, 18, No. 1, 147–164.

  5. Iskakov K.T., Romanov V.G., Karchevskiy A.L., Oralbekova Zh.O., Study of inverse problems for differential equations and numerical methods of their solving [in Russian], Astana, 2014.

  6. Lyashko S.I., Optimal control of coefficients for certain systems with distributed parameters, Differentsialnyye uravneniya, 1986, 22, No. 3, 458–462.

  7. Lyashko S.I., Nomirovskiy D.A., Sergienko T.I., Trajectory and terminal controllability in hyperbolic and pseudohyperbolic systems with the generalized impact, Kibernetika i sistemnyi analiz, 2001, No. 5, 157–166, 191–192.

  8. Lions J.L., Optimal control of systems, described by equations in partial derivatives [Russian translation], Mir, Moscow, 1972.

  9. Ladyzhenskaya O.A., Boundary value problems of mathematical physics [in Russian], Nauka, Moscow, 1973.

  10. Sobolev S.L., Some applications of the functional analysis in mathematical physics [in Russian], Nauka, Moscow, 1988.

  11. Vasiliev F.P., Methods of solving of extremal problems [in Russian], Nauka, Moscow, 1981.

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