The second boundary problem for the system hyperbolic type second order for large~$T$
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 3, pp. 94-99.

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In the paper we consider the control problem for objects which vibration are described by the system of ware equations with boundary condition of the second kind.
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S. V. Lexina. The second boundary problem for the system hyperbolic type second order for large~$T$. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 3, pp. 94-99. http://geodesic.mathdoc.fr/item/ISU_2011_11_3_a14/

[1] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1972 | MR | Zbl

[2] Shashkov A. G., Bubnov A. G., Yanovskii S. Yu., Volnovye yavleniya teploprovodnosti: Sistemno-strukturnyi podkhod, Editorial URSS, M., 2004, 296 pp.

[3] Gledvell G. M. L., Obratnye zadachi teorii kolebanii, NITs “Regulyarnaya i khaoticheskaya dinamika”, M.–Izhevsk, 2008, 608 pp.

[4] Arnold V. I., Lektsii ob uravneniyakh s chastnymi proizvodnymi, FAZIS, M., 1999, 180 pp. | MR

[5] Bitsadze A. V., Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981, 448 pp. | MR | Zbl

[6] Bullen K. E., Vvedenie v teoreticheskuyu seismologiyu, Mir, M., 1966, 460 pp.

[7] Romanovskii R. K., Zhukova O. G., “Giperbolicheskaya model zadachi granichnogo upravleniya protsessom teploperenosa v odnomernom tverdom materiale”, Dokl. AN VSh RF, 2006, no. 1(6), 69–77

[8] Goroshko O. A., Savin G. N., Vvedenie v mekhaniku deformiruemykh odnomernykh tel peremennoi dliny, Nauk. dumka, Kiev, 1971 | Zbl

[9] Goroshko O. A., Chizh A. A., “K voprosu o prodolno-krutilnykh kolebaniyakh uprugoi estestvenno zakruchennoi niti (kanata) peremennoi dliny s kontsevym gruzom, dvizhuschimsya po zhestkim napravlyayuschim”, Stalnye kanaty, Tekhnika, Kiev, 1964, 56–64

[10] Zhukova O. G., Romanovskii R. K., “Granichnoe upravlenie protsessom teploprovodnosti v odnomernom materiale. Giperbolicheskaya model”, Differentsialnye uravneniya, 43:5 (2007), 650–654 | MR | Zbl

[11] Zhukova O. G., Romanovskii R. K., “Dvustoronnee granichnoe upravlenie protsessom teploperenosa v odnomernom materiale. Giperbolicheskaya model”, Sibirskii zhurn. industrialnoi matematiki, 10:4 (2007), 32–40 | MR | Zbl

[12] Terletskii V. A., “K optimizatsii giperbolicheskikh sistem”, Metody optimizatsii i ikh prilozheniya, Tr. XII Baikalskoi mezhdunar. konf., v. 2, Irkutsk, 2001, 167–171

[13] Volterra V., “Sur les vibrations des corps elastiques isotropes”, Acta Math., 18 (1894), 161–232 | DOI | MR

[14] Adamar Zh., Zadacha Koshi dlya lineinykh uravnenii s chastnymi proizvodnymi giperbolicheskogo tipa, Fizmatlit, M., 1994, 544 pp.

[15] Burgatti P., “Sull' estensione del metodo d'integrazione di Riemann all' equazioni lineari d'ordine $n$ con due variabili independenti”, Rend. reale accad. lincei. Ser 5a, 15:2 (1906), 602–609 | Zbl

[16] Rellich F., “Verallgemeinerung der Riemannschen Integrtions-methode auf Differentialgleichungen $n$-ter Ordung in zwei Veränderlichen”, Math. Ann., 103 (1930), 249–278 | DOI | MR | Zbl

[17] Bianchi L., “Sulla estensione del metodo di Riemann alle equiazioni lineari alle derivate parziali d'ordine superiore”, Atti R. Accad. Lincei. Rend. Cl. Sc. fis., mat. e natur., 4:1 (1895), 133–142

[18] Bateman H., “Logarithmic solutions of Bianchi's equation”, Proc. USA Acad., 19 (1933), 852–854 | DOI | Zbl

[19] Zhegalov V. I., Mironov A. N., Differentsialnye uravneniya so starshimi chastnymi proizvodnymi, Kazan. mat. o-vo, Kazan, 2001, 226 pp.

[20] Holmgren E., “Sur les systemes lineaires aux derivees partielles du preimier ordre â daux variables independents â characteristiques reeles et distinotes”, Arkiv för Math., Astr. och Fysik., 5:1 (1906)

[21] Holmgren E., “Sur les systemes lineaires aux derivees partielles du preimier ordre â characteristiques reeles et distinctes”, Arkiv för Math., Astr. och Fysik., 6:2 (1909), 1–10

[22] Burmistrov B. N., “Reshenie zadachi Koshi metodom Rimana dlya sistemy uravnenii pervogo poryadka s vyrozhdeniem na granitse”, Tr. seminara po kraevym zadacham, 8, Izd-vo Kazansk. un-ta, Kazan, 1971, 41–54 | MR | Zbl

[23] Bitsadze A. V., “Vliyanie mladshikh chlenov na korrektnost postanovki kharakteristicheskikh zadach dlya giperbolicheskikh sistem vtorogo poryadka”, Dokl. AN SSSR, 225:1 (1975), 31–34 | MR | Zbl

[24] Andreev A. A., Volkodavov V. F., Shevchenko G. N., “O funktsii Rimana”, Differentsialnye uravneniya, Tr. pedinstitutov RSFSR, 4, 1974, 25–31

[25] Andreev A. A., “O postroenii funktsii Rimana”, Differentsialnye uravneniya: tr. pedinstitutov RSFSR, 6, 1975, 3–9 | MR

[26] Andreev A. A., “Ob odnom klasse sistem differentsialnykh uravnenii giperbolicheskogo tipa”, Differentsialnye uravneniya: tr. pedinstitutov RSFSR, 16, 1980, 3–5

[27] Muskhelishvili N. I., Nekotorye osnovnye zadachi matematicheskoi teorii uprugosti, Izd-vo AN SSSR, M., 1954 | Zbl

[28] Koshlyakov N. S., Gliner E. B., Smirnov M. M., Uravneniya v chastnykh proizvodnykh matematicheskoi fiziki, Vyssh. shk., M., 1970, 712 pp. | Zbl

[29] Ames W. F., Nonlinear Partial differential equations in engineering, Academic Press, N.Y.–L., 1965 | MR | Zbl

[30] Leksina S. V., “Zadacha granichnogo upravleniya v usloviyakh vtoroi kraevoi zadachi dlya matrichnogo volnovogo uravneniya”, Vestn. SamGU. Estestvennonauch. ser., 2009, no. 4(70), 20–29