Geodesic
Optimal control of the melting process and solidification of a substance
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 44 (2004) no. 8, pp. 1364-1379 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_2004_44_8_a3,
     author = {A. F. Albu and V. I. Zubov and V. A. Inyakin},
     title = {Optimal control of the melting process and solidification of a substance},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1364--1379},
     year = {2004},
     volume = {44},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_8_a3/}
}
TY  - JOUR
AU  - A. F. Albu
AU  - V. I. Zubov
AU  - V. A. Inyakin
TI  - Optimal control of the melting process and solidification of a substance
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2004
SP  - 1364
EP  - 1379
VL  - 44
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_8_a3/
LA  - ru
ID  - ZVMMF_2004_44_8_a3
ER  - 
%0 Journal Article
%A A. F. Albu
%A V. I. Zubov
%A V. A. Inyakin
%T Optimal control of the melting process and solidification of a substance
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2004
%P 1364-1379
%V 44
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_8_a3/
%G ru
%F ZVMMF_2004_44_8_a3
A. F. Albu; V. I. Zubov; V. A. Inyakin. Optimal control of the melting process and solidification of a substance. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 44 (2004) no. 8, pp. 1364-1379. http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_8_a3/

[1] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[2] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976 | MR | Zbl

[3] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1977

[4] Godunov S. K., Uravneniya matematicheskoi fiziki, Nauka, M., 1979 | MR | Zbl

[5] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[6] Ahmed N. U., Teo K. L., Optimal control of distributed parameter systems, North Holland, New York–Oxford, 1981 | MR | Zbl

[7] Karslou G., Eger D., Teploprovodnost tverdykh tel, Nauka, M., 1964

[8] Lykov A. V., Teoriya teploprovodnosti, Vyssh. shkola, M., 1967 | Zbl

[9] Kartashov E. M., Analiticheskie metody v teorii teploprovodnosti tverdykh tel, Vyssh. shkola, M., 2001

[10] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1977 | MR | Zbl

[11] Butkovskii A. G., Teoriya optimalnogo upravleniya sistemami s raspredelennymi parametrami, Nauka, M., 1975 | MR

[12] Butkovskii A. G., Metody upravleniya sistemami s raspredelennymi parametrami, Nauka, M., 1975

[13] Lure K. A., Optimalnoe upravlenie v zadachakh matematicheskoi fiziki, Nauka, M., 1975 | MR

[14] Lions Zh.–L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami v chastnykh proizvodnykh, Mir, M., 1972 | MR

[15] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981 | MR

[16] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002

[17] Egorov A. I., Optimalnoe upravlenie teplovymi i diffuzionnymi protsessami, Nauka, M., 1978 | MR

[18] Morozkin N. F., Optimalnoe upravlenie protsessami nagreva s uchetom fazovykh ogranichenii, Izd-vo Bashkirskogo un-ta, Ufa, 1997

[19] Ivanovich L. D., “Raznostnaya approksimatsiya i regulyarizatsiya zadachi ob optimalnom nagreve sterzhnya”, Vestn. MGU. Ser. 15. Vychisl. matem. i kibernetika, 1982, no. 3, 10–15 | MR | Zbl

[20] Samarskii A. A., Moiseenko B. D., “Ekonomichnaya skhema skvoznogo scheta dlya mnogomernoi zadachi Stefana”, Zh. vychisl. matem. i matem. fiz., 5:5 (1965), 816–827 | MR

[21] Budak B. M., Soloveva E. N., Uspenskii A. B., “Raznostnyi metod so sglazhivaniem koeffitsientov dlya resheniya zadach Stefana”, Zh. vychisl. matem. i matem. fiz., 5:5 (1965), 828–840 | MR | Zbl

[22] Vasilev F. P., “Ob odnom variante metoda pryamykh dlya resheniya zadach tipa Stefana”, Vychisl. metody i programmirovanie, VIII, Izd-vo MGU, M., 1967, 139–164

[23] Vasilev F. P., “O metode pryamykh dlya resheniya odnofaznoi zadachi tipa Stefana”, Zh. vychisl. matem. i matem. fiz., 8:1 (1968), 64–78

[24] Bachelis R. D., Melamed V. G., Shlyaifer D. B., “Reshenie zadachi tipa Stefana metodom pryamykh”, Zh. vychisl. matem. i matem. fiz., 9:3 (1969), 585–594 | Zbl

[25] Rose M., “A method for calculating solutions of parabolic equations with a free boundary”, Math. Comput., 14 (1960), 249–256 | DOI | MR | Zbl

[26] White R. E., “An enthalpy formulation of the Stephan problem”, SIAM J. Numer. Analys., 19:6 (1982), 1129–1157 | DOI | MR | Zbl

[27] White R. E., “A numerical solution of the enthalpy formulation of the Stephan problem”, SIAM J. Numer. Analys., 19:6 (1982), 1158–1172 | DOI | MR | Zbl

[28] Darin H. A., Mazhukin V. I., “Matematicheskoe modelirovanie zadachi Stefana na adaptivnoi setke”, Differents. ur-niya, 23:7 (1987), 1154–1160 | MR

[29] Yurii A. D., “Ob odnoi optimalnoi zadache tipa Stefana”, Dokl AN SSSR, 251:6 (1980), 1317–1321 | MR

[30] Goldman N. L., Obratnye zadachi Stefana. Teoriya i metody resheniya, Izd-vo MGU, M., 1999

[31] Albu A. F., Gorbunov V. I., Zubov V. I., “Optimalnoe upravlenie protsessom plavleniya”, Zh. vychisl. matem. i matem. fiz., 40:4 (2000), 517–531 | MR | Zbl

[32] Albu A. F., Zubov V. I., “Optimalnoe upravlenie protsessom kristallizatsii veschestva”, Zh. vychisl. matem. i matem. fiziki, 44:1 (2004), 38–50 | MR | Zbl

[33] Evtushenko Y. G., “Computation of exact gradients in distributed dynamic systems”, Optimizat. Methods and Software, 9 (1998), 45–75 | DOI | MR | Zbl

[34] Albu A. F., Zubov V. I., “O modifikatsii odnoi skhemy dlya rascheta protsessa plavleniya”, Zh. vychisl. matem. i matem. fiz., 41:9 (2001), 1434–1443 | MR | Zbl

[35] Albu A. F., Gorbunov V. I., Zubov V. I., “Ob optimalnom upravlenii protsessom plavleniya”, Matem. modelirovanie, 12:5 (2000), 114–118 | Zbl

[36] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR

[37] Moiseev N. N., Ivanilov Yu. P., Stolyarova E. M., Metody optimizatsii, Nauka, M., 1978