Geodesic
On the definition of a time-dependent lower coefficient in a third-order hyperbolic equation
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 34 (2021) no. 1, pp. 9-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper deals with an inverse problem for a hyperbolic equation of the third order. An inverse problem is posed, which consists in determining an unknown coefficient that depends on time. As additional information for solving the inverse problem, we set the values of the solution to the problem at an interior point, and prove the existence and uniqueness theorem for the solution of the inverse problem. The proof is based on the derivation of a nonlinear system of integral equations of the Volterra type of the second kind and the proof of its solvability.
Keywords: hyperbolic equation, uniqueness
Mots-clés : inverse coefficient problem, existence, Volterra equation. 
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B. S. Ablabekov; A. K. Goroev. On the definition of a time-dependent lower coefficient in a third-order hyperbolic equation. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 34 (2021) no. 1, pp. 9-18. http://geodesic.mathdoc.fr/item/VKAM_2021_34_1_a0/

[1] Barenblatt G. I., Zheltov Iu. P., Kochina I. N., “Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks”, PMM, 24:5 (1960), 852-864

[2] Hallaire M., “L’eau et la productions vegetable”, Institut National de la Recherche Agronomique, 9 (1964)

[3] Chudnovsky A. F., Thermophysics of the soil, Moscow, Nauka, 1976, 352 pp.

[4] Dzektser E. S., “Equation of motion of underground water with a free surface in multilayer media”, Dokl. Akad. Nauk SSSR, 220:3 (1975), 540–543

[5] Rudenko O. V., Soluyan S. I., Theoretical Principles of Nonlinear Acoustics, Moscow, Nauka, 1975

[6] Ablabekov B. S.,Asanov A. R., Kurmanbaeva A. K., “Inverse problems for equation of the third order equations”, Ilim, Bishkek, 2011, 156 pp.

[7] Ablabekov B. S., Joroev A. K., “O razreshimosti zadachi Cauchy dlja hyperbolicheskogo uravnenija”, Evrazijskoe Nauchnoe Obedinenie, 1:5(51) (2019), 1-4

[8] Ablabekov B. S., Inverse problems for pseudoparabolic Equations, Ilim, Bishkek, 2001, 183 pp.

[9] Zikirov O. S., “O kraevykh zadachakh dlya giperbolicheskogo uravneniya tret'ego poryadka”, Doklady Adygskoy (Cherkesskoy) Mezhdunarodnoy akademii nauk, 9:1 (2007), 45–48 | MR

[10] Zikirov O. S., “Local and nonlocal boundary-value problems for third-orderhyperbolic equations”, Journal of Mathematical Sciences, 175:1 (2011), 104-123

[11] Denisov A. M., “Integro-functional equations in the inverse source problem for the wave equation”, Differ. Equat., 42:9 (2006), 1221–1232 | MR

[12] Romanov V. G., Inverse Problems of Mathematical Physics, VNU Science Press, Utrecht, 1987

[13] Romanov V. G., Ustoychivost' v obratnykh zadachakh, Nauchnyy mir, Moskva, 2005, 296 pp.