An algorithm for dynamic reconstruction of the right-hand side of a second-order equation with distributed parameters
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1255-1269 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The dynamic reconstruction of the right-hand side of a second-order differential equation is considered. A solution algorithm is proposed that is robust to information noise and computational errors. The algorithm is constructed using dynamic inversion theory.
@article{ZVMMF_2017_57_8_a2,
     author = {V. I. Maksimov},
     title = {An algorithm for dynamic reconstruction of the right-hand side of a second-order equation with distributed parameters},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1255--1269},
     year = {2017},
     volume = {57},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a2/}
}
TY  - JOUR
AU  - V. I. Maksimov
TI  - An algorithm for dynamic reconstruction of the right-hand side of a second-order equation with distributed parameters
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 1255
EP  - 1269
VL  - 57
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a2/
LA  - ru
ID  - ZVMMF_2017_57_8_a2
ER  - 
%0 Journal Article
%A V. I. Maksimov
%T An algorithm for dynamic reconstruction of the right-hand side of a second-order equation with distributed parameters
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 1255-1269
%V 57
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a2/
%G ru
%F ZVMMF_2017_57_8_a2
V. I. Maksimov. An algorithm for dynamic reconstruction of the right-hand side of a second-order equation with distributed parameters. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1255-1269. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a2/

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

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

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

[4] Kryazhimskii A. V., Osipov Yu. S., “O modelirovanii upravleniya v dinamicheskoi sisteme”, Izv. AN SSSR. Tekhn. kibernetika, 2 (1983), 51–60 | Zbl

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

[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., Vasilev F. P., Potapov M. M., Osnovy metoda dinamicheskoi regulyarizatsii, MGU, M., 1999

[8] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1984

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

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

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

[12] Osipov Yu. S., Kryazhimskii A. V., Maksimov V. I., “Metod ekstremalnogo sdviga N. N. Krasovskogo i zadachi granichnogo upravleniya”, Avtomatika i telemekhan., 4:5 (2009), 18–30

[13] Maksimov V. I., “O vosstanovlenii vkhodov v lineinykh parabolicheskikh uravneniyakh”, Tr. In-ta matem. i mekhan. UrO RAN, 17, no. 5, 2011, 125–135

[14] Kryazhimskii A. V., Maksimov V. I., “On rough inversion of a dynamical system with a disturbance”, J. Inv. Ill-Posed Problems, 16:5 (2008), 1–14 | MR

[15] Maksimov V. I., Osipov Yu. S., “O granichnom upravlenii raspredelennoi sistemoi na beskonechnom promezhutke vremeni”, Zh. vychisl. matem. i matem. fiz., 56:1 (2016), 14–26 | Zbl

[16] Maksimov V. I., “Ob odnom algoritme otslezhivaniya resheniya parabolicheskogo uravneniya na beskonechnom promezhutke vremeni”, Differents. ur-niya, 50:5 (2014), 366–375 | DOI | Zbl

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