Methods of constructing approximate self-similar solutions of nonlinear heat equations. II

V. A. Galaktionov   ; A. A. Samarskii

Sbornik. Mathematics, Tome 46 (1983) no. 4, pp. 439-458

Bibliographie

[1] Galaktionov V. A., Samarskii A. A., “Metody postroeniya priblizhennykh avtomodelnykh reshenii nelineinykh uravnenii teploprovodnosti. 1”, Matem. sb., 118 (160) (1982), 292–322

[2] Kruzhkov S. N., “Obobschennye resheniya nelineinykh uravnenii pervogo poryadka i nekotorye zadachi dlya kvazilineinykh parabolicheskikh uravnenii”, Vestn. MGU, mat. mekh., 1964, no. 6, 65–74

[3] Kruzhkov S. N., Nelokalnaya teoriya uravnenii Gamiltona–Yakobi (Trudy Vsesoyuzn. konf. po uravn. s chastn. proizv., posv. 75-letiyu akad. I. G. Petrovskogo), Izd-vo MGU, M., 1978 | MR

[4] Galaktionov V. A., “O priblizhennykh avtomodelnykh resheniyakh uravnenii tipa nelineinoi teploprovodnosti”, Diff. uravneniya, 16:9 (1980), 1660–1676 | MR | Zbl

[5] Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P., Samarskii A. A., Deistvie granichnykh rezhimov s obostreniem na sredu s postoyannoi teploprovodnostyu, Preprint IPM AN SSSR. No 28, IPM, M., 1979

[6] Samarskii A. A., “O novykh metodakh issledovaniya asimptoticheskikh svoistv parabolicheskikh uravnenii”, Trudy Matem. in-ta im. V. A. Steklova AN SSSR, 158 (1981), 153–162 | MR | Zbl

[7] Samarskii A. A., Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P., “Lokalizatsiya protsessov diffuzii v sredakh s postoyannymi svoistvami”, DAN SSSR, 247:2 (1979), 349–352 | MR

[8] Galaktionov V. A., “Priblizhennye avtomodelnye resheniya uravneniya teploprovodnosti”, DAN SSSR, 1982

[9] Ovsyannikov L. V., “Gruppovye svoistva uravneniya nelineinoi teploprovodnosti”, DAN SSSR, 125:3 (1959), 492–495 | Zbl

[10] Dorodnitsyn V. A., Gruppovye svoistva i invariantnye resheniya uravneniya nelineinoi teploprovodnosti s istochnikom ili stokom, Preprint IPM AN SSSR. No 57, IPM, M., 1979 | MR

[11] Kurdyumov S. P., Lokalizatsiya diffuzionnykh protsessov i vozniknovenie struktur pri razvitii v dissipativnoi srede rezhimov s obostreniem, Diss. na soiskanie uch. st. dokt. fiz.-matem. nauk, Institut prikl. matem. im. M. V. Keldysha AN SSSR, M., 1979

[12] Zmitrenko N. V., Kurdyumov S. P., Mikhailov A. P., Samarskii A. A., Vozniknovenie struktur v nelineinykh sredakh i nestatsionarnaya termodinamika rezhimov s obostreniem, Preprint IPM AN SSSR. No 74, IPM, M., 1976 | MR

[13] Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P., Samarskii A. A., O neogranichennykh resheniyakh polulineinykh parabolicheskikh uravnenii, Preprint IMP AN SSSR. No 161, IPM, M., 1979

[14] Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P., Samarskii A. A., “Lokalizatsiya tepla v nelineinykh sredakh”, Diff. uravneniya, 17:10 (1981), 1826–1841 | MR | Zbl

[15] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1972 | MR

[16] Nikiforov A. F., Uvarov V. B., Spetsialnye funktsii matematicheskoi fiziki, Nauka, M., 1978 | MR

[17] Lie S., “Über die integration durch bestimmte integrale von einer classer linearer partiellen differentialgleichungen”, Arch. Math., 6 (1881), 328–368

[18] Galaktionov V. A., “Ob usloviyakh lokalizatsii neogranichennykh reshenii kvazilineinykh parabolicheskikh uravnenii”, DAN SSSR, 264:5 (1982) | MR | Zbl