Geodesic
Dynamic reconstruction of the right-hand side of a hyperbolic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 1008-1019 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A hyperbolic equation subject to external disturbances is considered. It is assumed that its solution can be measured (possibly with some errors). Algorithms for recovering (reconstructing) the disturbances from the measurements are described. The algorithms are robust to observational and computational errors. 
@article{ZVMMF_2015_55_6_a8,
     author = {V. I. Maksimov},
     title = {Dynamic reconstruction of the right-hand side of a hyperbolic equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1008--1019},
     year = {2015},
     volume = {55},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a8/}
}
TY  - JOUR
AU  - V. I. Maksimov
TI  - Dynamic reconstruction of the right-hand side of a hyperbolic equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 1008
EP  - 1019
VL  - 55
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a8/
LA  - ru
ID  - ZVMMF_2015_55_6_a8
ER  - 
%0 Journal Article
%A V. I. Maksimov
%T Dynamic reconstruction of the right-hand side of a hyperbolic equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 1008-1019
%V 55
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a8/
%G ru
%F ZVMMF_2015_55_6_a8
V. I. Maksimov. Dynamic reconstruction of the right-hand side of a hyperbolic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 1008-1019. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a8/

[1] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Nauka, M., 1978

[2] Osipov Yu. S., Vasilev F. P., Potapov M. M., Osnovy metoda dinamicheskoi regulyarizatsii, Izd-vo MGU, M., 1999

[3] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1978

[4] Lavrentev M. M., Romanov V. G., Shishatskii S. P., Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka, M., 1980 | MR

[5] Prilepko A. I., Orlovsky D. G., Vasin I. A., Methods for solving inverse problems in mathematical physics, New York–Basel, 1999 | MR

[6] Osipov Yu. S., Kryazhimskii A. V., Inverse problems for ordinary differential equations: dynamical solutions, Gordon and Breach, New York, 1995 | MR | Zbl

[7] Osipov Yu. S., Kryazhimskii A. V., Maksimov V. I., Metody dinamicheskogo vosstanovleniya vkhodov upravlyaemykh sistem, UrO RAN, Ekaterinburg, 2011

[8] Osipov Yu. S., Kryazhimskii A. V., Maksimov V. I., “Obratnye zadachi dinamiki dlya parabolicheskikh sistem”, Differents. ur-niya, 36:5 (2000), 579–597 | MR | Zbl

[9] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974 | MR

[10] Osipov Yu. S., Izbrannye trudy, MGU, M., 2009

[11] Osipov Yu. S., On the reconstruction of a parameter for a hyperbolic system, IIASA Working Paper WP-91-054, 1991

[12] Maksimov V. I., “Ustoichivoe vosstanovlenie vkhodnykh vozdeistvii po rezultatam izmerenii”, Avtomatika, 4 (1990), 60–65 ; 6, 19–24 | Zbl | MR | Zbl

[13] Maksimov V. I., “Approximation of an inverse problem for variational inequalities”, Differential and Integral Equations, 8:8 (1995), 1367–1379 | MR

[14] Maksimov V. I., Zadachi dinamicheskogo vosstanovleniya vkhodov beskonechnomernykh sistem, UrO RAN, Ekaterinburg, 2000

[15] Maksimov V. I., “Some dynamical inverse problems for hyperbolic systems”, Control and Cybernetics, 25:3 (1996), 465–481 | MR | Zbl

[16] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977 | MR