Non-self-similar solutions of multidimensional nonlinear diffusion equations

G. A. Rudykh ; È. I. Semenov

Matematičeskie zametki, Tome 67 (2000) no. 2, pp. 250-256.

Bibliographie

[1] Kershner R., “O nekotorykh svoistvakh obobschennykh reshenii kvazilineinykh vyrozhdayuschikhsya parabolicheskikh uravnenii”, Acta Math. Hungar., 32:3–4 (1978), 301–330 | MR | Zbl

[2] Galaktionov V. A., Dorodnitsyn V. A., Elenin G. G., Kurdyumov S. P., Samarskii A. A., “Kvazilineinoe uravnenie teploprovodnosti: obostrenie, lokalizatsiya, simmetriya, tochnye resheniya, asimptotiki, struktury”, Itogi nauki i tekhn. Sovrem. probl. matem. Noveishie dostizheniya, 28, VINITI, M., 1987, 95–205

[3] Samarskii A. A., Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P., Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii, Nauka, M., 1987

[4] Galaktionov V. A., Posashkov S. A., “O novykh tochnykh resheniyakh parabolicheskikh uravnenii s kvadratichnymi nelineinostyami”, ZhVMiMF, 29:4 (1989), 497–506. | MR

[5] Galaktionov V. A., “On new exact blow-up solutions for nonlinear heat conduction equations with source and applications”, Differential Integral Equations, 3:5 (1990), 863–874 | MR | Zbl

[6] Galaktionov V. A., Invariant subspaces and new explicit solution to evolution equations with quadratic nonlinearities, School of Math. Report No AM-91-11, Univ. Bristol, 1991

[7] Galaktionov V. A., “Invariant subspaces and new explicit solution to evolution equations with quadratic nonlinearities”, Proc. Roy. Soc. Edinburgh Sect. A, 125 (1995), 225–246 | MR | Zbl

[8] King J. R., “Exact multidimensional solutions to some nonlinear diffusion equations”, Quart. J. Mech. Appl. Math., 46:3 (1993), 419–436 | DOI | MR | Zbl

[9] Pukhnachev V. V., “Mnogomernye tochnye resheniya uravneniya nelineinoi diffuzii”, Prikl. mekhanika i tekhnich. fizika, 36:2 (1995), 23–31 | MR | Zbl

[10] Meirmanov A. M., Pukhnachev V. V., Shmarev S. I., Evolution Equations and Lagrangian Coordinates, de Gruyter, Berlin–New York, 1997 | Zbl

[11] Kosygina E. R., “Ob anizotropnykh tochnykh resheniyakh mnogomernogo uravneniya nestatsionarnoi filtratsii”, ZhVMiMF, 35:2 (1995), 241–259 | MR | Zbl

[12] Rudykh G. A., Semenov E. I., “Novye tochnye resheniya odnomernogo uravneniya nelineinoi diffuzii”, Sib. matem. zh., 38:5 (1997), 1130–1139 | MR | Zbl

[13] Rudykh G. A., Semenov E. I., “O novykh tochnykh resheniyakh odnomernogo uravneniya nelineinoi diffuzii s istochnikom (stokom)”, ZhVMiMF, 38:6 (1998), 971–977 | MR | Zbl

[14] Kalashnikov A. S., “Nekotorye voprosy kachestvennoi teorii nelineinykh vyrozhdayuschikhsya parabolicheskikh uravnenii vtorogo poryadka”, UMN, 42:2 (1987), 135–176 | MR | Zbl

[15] Rudykh G. A., Semenov E. I., “Tochnye neotritsatelnye resheniya mnogomernogo uravneniya nelineinoi diffuzii”, Sib. matem. zh., 39:5 (1998), 1129–1138 | MR

[16] Rudykh G. A., Semenov E. I., “Tochnye neavtomodelnye resheniya uravneniya $u_t=\Delta \ln u$”, Matem. zametki (to appear)

[17] Rudykh G. A., Semenov E. I., “Tochnye resheniya mnogomernogo uravneniya nelineinoi diffuzii”, Izv. RAN. Ser. matem. (to appear)

[18] Galaktionov V. A., Posashkov S. A., Svirschevskii S. R., “Obobschennoe razdelenie peremennykh dlya differentsialnykh uravnenii s polinomialnymi nelineinostyami”, Differents. uravneniya, 31:2 (1995), 253–261 | MR | Zbl

[19] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii, Nauka, M., 1978 | Zbl

[20] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978

[21] Ibragimov N. Kh., Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983

[22] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989

[23] Akhiezer N. I., Elementy teorii ellipticheskikh funktsii, Gostekhizdat, M., 1948