The boundary control problem for the system of wave equations
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2008), pp. 5-10.

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In the paper we consider the control problem for objects which vibration are discribed by ware equation system with boundary condition of the first type. Nessesary condition on function determininy initial and final conditions are obtained.
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A. A. Andreev; S. V. Leksina. The boundary control problem for the system of wave equations. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2008), pp. 5-10. http://geodesic.mathdoc.fr/item/VSGTU_2008_1_a0/

[1] Znamenskaya L. N., Upravlenie uprugimi kolebaniyami, Fizmatlit, M., 2004 | Zbl

[2] Butkovskii A. G., Teoriya optimalnogo upravleniya sistemami s raspredelennymi parametrami, Nauka, M., 1965 | MR | Zbl

[3] Ilin V. A., “Volnovoe uravnenie s granichnym upravleniem na dvukh kontsakh za proizvolnyi promezhutok vremeni”, Differentsialnye uravneniya, 35:11 (1999), 1517–1534 | MR

[4] Ilin V. A., “Granichnoe upravlenie protsessom kolebanii na dvukh kontsakh”, Dokl. RAN, 369:5 (1999), 592–596 | MR

[5] Ilin V. A., “Granichnoe upravlenie protsessom kolebanii na odnom kontse pri zakreplennom vtorom kontse”, Dokl. RAN, 369:6 (1999), 732–735 | MR

[6] Ilin V. A., “Volnovoe uravnenie s granichnym upravleniem na odnom kontse pri zakreplennom vtorom kontse”, Differentsialnye uravneniya, 35:12 (1999), 1640–1659 | MR

[7] Ilin V. A., Moiseev E. I., “Granichnoe upravlenie radialno-simmetrichnymi kolebaniyami krugloi membrany”, Dokl. RAN, 393:6 (2003), 730–734 | MR

[8] Nikitin A. A., “Granichnoe upravlenie uprugoi siloi na odnom kontse struny”, Dokl. RAN, 406:4 (2006), 458–461 | MR

[9] Sabitova Yu. K., “O gladkosti resheniya zadachi granichnogo upravleniya na dvukh kontsakh dlya uravneniya struny”, Differentsialnye uravneniya, 42:1 (2006), 133–134 | DOI | MR

[10] Ilin V. A., Tikhomirov V. V., “Volnovoe uravnenie s kraevym upravleniem”, Differentsialnye uravneniya, 35:1 (1999), 137–138

[11] Znamenskaya L. N., “Upravlenie kolebaniyami struny v klasse obobschennykh reshenii iz $L_2$”, Differentsialnye uravneniya, 38:5, 666–672 \year 2002 | DOI | MR | Zbl

[12] Borovskikh A. V., “Formuly granichnogo upravleniya neodnorodnoi strunoi, I”, Differentsialnye uravneniya, 43:1 (2007), 64–89 | DOI | MR | Zbl

[13] Borovskikh A. V., “Formuly granichnogo upravleniya neodnorodnoi strunoi, II”, Differentsialnye uravneniya, 43:5 (2007), 640–649 | DOI | MR | Zbl

[14] Ilin V. A., “O granichnom upravlenii protsessom, opisyvaemym uravneniem $k(x)[k(x)u_x(x,t)]_x-u_{tt}(x,t)=0$”, Dokl. RAN, 386:2 (2002), 156–159 | MR

[15] Andreev A. A., Leksina S. V., “O granichnom upravlenii sistemy prodolno-krutilnykh kolebanii”, Differentsialnye uravneniya i ikh prilozheniya, SamDiff-2007. Tez. konf., Univers grupp, Samara, 2007, 21–25

[16] Leksina S. V., “Analog formuly Dalambera dlya sistemy volnovykh uravnenii”, Differentsialnye uravneniya, teoriya funktsii i prilozheniya, Tez. dokl. Mezhdunarod. konf-tsii, posvyaschennoi 100-letiyu so dnya rozhdeniya akad. I. N. Vekua (Novosibirsk, 26.05–02.06.2007 g.), Novosibir. gos. un-t, Novosibirsk, 2007

[17] 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, T. 1, Tekhnika, Kiev, 1964, 56–64

[18] Goroshko O. A., Savin G. N., Vvedenie v mekhaniku deformiruemykh odnomernykh tel peremennoi dliny, Naukova dumka, Kiev, 1971