Geodesic
Inverse problems of the determination of external sources in the equation of longitudinal wave propagation
Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 3, pp. 28-40.

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We consider inverse problems for the equation of longitudinal wave propagation with overdetermination conditions of final and integral types. The main purpose of the research is the proof of the existence of regular solutions to the inverse determination problems together with the solution of the also unknown external sources. One of the proposed approaches is based on the reduction of the inverse problem to an integro-differential equation.
Keywords: equation of longitudinal wave propagation, inverse problem, integro-differential equation, a priori estimate, regular solution, uniqueness.
Mots-clés : existence 
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G. V. Namsaraeva. Inverse problems of the determination of external sources in the equation of longitudinal wave propagation. Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 3, pp. 28-40. http://geodesic.mathdoc.fr/item/SJIM_2016_19_3_a2/

[1] Longren K., “Eksperimentalnye issledovaniya solitonov v nelineinykh liniyakh peredachi s dispersiei”, Solitony v deistvii, Mir, M., 1981, 138–162

[2] Ikezi Kh., “Eksperimentalnoe issledovanie solitonov v plazme”, Solitony v deistvii, Mir, M., 1981, 163–184

[3] Uizem Dzh., Lineinye i nelineinye volny, Mir, M., 1977 | MR

[4] Demidenko G. V., Uspenskii S. V., Uravneniya i sistemy, ne razreshennye otnositelno starshei proizvodnoi, Nauch. kniga, Novosibirsk, 1998 | MR

[5] Utkina E. A., “Edinstvennost resheniya zadachi Dirikhle dlya odnogo $n$-mernogo psevdoparabolicheskogo uravneniya”, Differents. uravneniya, 48:10 (2012), 1443–1449 | MR | Zbl

[6] Prilepko A. I., Orlovsky D. G., Vasin I. A., Methods for Solving Inverse Problems in Mathematical Physics, Marcell Dekker, New York–Basel, 2000 | MR | Zbl

[7] Anikonov Yu. E., Inverse and Ill-Posed Problems, VSP, Utrecht, 1997 | MR | Zbl

[8] Ivanchov M., Inverse Problems for Equations of Parabolic Type, Mathematical Studies: Monograph Series, 10, 2003 | MR | Zbl

[9] Belov Yu. Ya., Inverse Problems for Partial Differential Equations, VSP, Utrecht, 2002 | MR | Zbl

[10] Kozhanov A. I., Composite Type Equations and Inverse Problems, VSP, Utrecht, 1999 | MR | Zbl

[11] Megraliev Ya. T., “Obratnaya kraevaya zadacha dlya uravneniya Bussineska–Lyava s dopolnitelnym integralnym usloviem”, Sib. zhurn. industr. matematiki, 16:1 (2013), 75–83 | MR | Zbl

[12] Megraliev Ya. T. Alizade F. Kh., “Obratnaya kraevaya zadacha dlya odnogo uravneniya Bussineska s integralnym usloviem”, Chebyshevskii sb., 14:4 (2013), 167–179 | MR

[13] Kasymalieva A. A., Obratnye zadachi dlya uravneniya Bussineska–Lyava, Avtoref. dis. $\dots$ kand. fiz.-mat. nauk: 01.01.02, Bishkek, 2014, 15 pp.

[14] Kozhanov A. I., “O razreshimosti obratnykh zadach vosstanovleniya koeffitsientov v uravneniyakh sostavnogo tipa”, Vestn. NGU. Ser. Matematika, mekhanika, informatika, 8:2 (2008), 81–99 | Zbl

[15] Nakhushev A. M., Nagruzhennye uravneniya i ikh primenenie, Nauka, M., 2012

[16] Dzhenaliev M. T., K teorii lineinykh kraevykh zadach dlya nagruzhennykh differentsialnykh uravnenii, Izd-vo In-ta teor. i priklad. matematiki, Almaty, 1995

[17] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 1980 | MR

[18] Yakubov S. Ya., Lineinye differentsialno-operatornye uravneniya i ikh prilozheniya, Elm, Baku, 1985