Geodesic
Optimal two-sided boundary control of heat transmission in a~rod. Hyperbolic model
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 54-60.

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We consider mixed problem for one-dimensional hyperbolic system of thermal conductivity equations. We construct a class of boundary controls that provide given distribution on phase vector $(T,q)$ in a given moment of time. From this class we choose a control by the Lagrange method that minimize a square functional of loss.
Keywords: hyperbolic conductivity, boundary phase vector control, reduction of boundary control to starting one, Riemann matrices of first and second kind. 
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     author = {R. K. Romanovskii and Yu. A. Medvedev},
     title = {Optimal two-sided boundary control of heat transmission in a~rod. {Hyperbolic} model},
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R. K. Romanovskii; Yu. A. Medvedev. Optimal two-sided boundary control of heat transmission in a~rod. Hyperbolic model. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 54-60. http://geodesic.mathdoc.fr/item/IVM_2016_6_a5/

[1] Romanovskii R. K., “O matritsakh Rimana pervogo i vtorogo roda”, Matem. sb., 127(169):4 (1985), 494–501 | MR | Zbl

[2] Vorobeva E. V., Romanovskii R. K., “Metod kharakteristik dlya giperbolicheskikh kraevykh zadach na ploskosti”, Sib. matem. zhurn., 41:3 (2000), 531–540 | MR | Zbl

[3] Romanovskii R. K., Vorobeva E. V., Stratilatova E. N., Metod Rimana dlya giperbolicheskikh sistem, Nauka, Novosibirsk, 2007

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

[5] Romanovskii R. K., Zhukova O. G., “Granichnoe upravlenie protsessom teploperenosa v dvumernom materiale. Giperbolicheskaya model”, Sib. zhurn. industrialnoi matem., 11:3 (2008), 119–125 | MR

[6] Zhukova O. G., “Granichnoe upravlenie protsessom teploperenosa v trekhmernom materiale. Giperbolicheskaya model”, Differents. uravneniya, 45:12 (2009), 650–654 | MR

[7] Romanovskii R. K., Churasheva N. G., “Optimalnoe granichnoe upravlenie protsessom teploperenosa v odnomernom materiale. Giperbolicheskaya model”, Differents. uravneniya, 48:9 (2012), 1256–1264 | MR | Zbl

[8] Romanovskii R. K., Churasheva N. G., “Optimalnoe granichnoe upravlenie giperbolicheskoi sistemoi uravnenii teploprovodnosti”, Dokl. RAN, 446:2 (2012), 138–141 | MR | Zbl

[9] Romanovskii R. K., Churasheva N. G., “Optimalnoe granichnoe upravlenie teploperenosom v trekhmernom materiale. Giperbolicheskaya model”, Differents. uravneniya, 50:3 (2014), 385–393 | DOI | MR | Zbl

[10] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Nauka, M., 1979 | MR

[11] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1999 | MR

[12] Smirnov V. I., Kurs vysshei matematiki, v. 4, ch. 1, Nauka, M., 1974 | MR

[13] Zabreiko P. P., Koshelev A. I., Krasnoselskii M. A. i dr., Integralnye uravneniya, Nauka, M., 1968 | MR