Solution of nonlinear equations in analytic polyalgebras.~I

S. S. Titov

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2000), pp. 66-76.

Bibliographie

[1] Vasin V. V., Sidorov A. F., “O nekotorykh metodakh priblizhennogo resheniya differentsialnykh i integralnykh uravnenii”, Izv. vuzov. Matematika, 1983, no. 7, 13–27 | MR | Zbl

[2] Bukhshtaber V. M., Mischenko A. S., Novikov S. P., “Formalnye gruppy i ikh rol v apparate algebraicheskoi topologii”, UMN, 26:2 (1971), 131–154 | MR | Zbl

[3] Pate T. H., “A direct iterative method for an abstract Cauchy–Kowalewsky theorem”, Indiana Univ. Math. J., 30:3 (1981), 415–425 | DOI | MR | Zbl

[4] Kovalevskaya S. V., Nauchnye raboty, Izd-vo AN SSSR, M., 1948, 368 pp. | MR

[5] Grauert G., Remmert R., Analiticheskie lokalnye algebry, Nauka, M., 1988, 303 pp. | MR | Zbl

[6] Ovsyannikov L. V., “Singulyarnyi operator v shkale banakhovykh prostranstv”, DAN SSSR, 163:4 (1965), 819–822 | MR | Zbl

[7] Ovsyannikov L. V., “Nelineinaya zadacha Koshi v shkale banakhovykh prostranstv”, DAN SSSR, 200:4 (1971), 789–792 | Zbl

[8] Treves F., “On the theory of linear partial differential operators with analytic coefficients”, Trans. Amer. Math. Soc., 137 (1969), 1–20 | DOI | MR | Zbl

[9] Treves F., “An abstract nonlinear Cauchy–Kovalewska theorem”, Trans. Amer. Math. Soc., 150:1 (1970), 77–92 | DOI | MR | Zbl

[10] Nirenberg L., “An abstract form of the nonlinear Cauchy–Kowalewski theorem”, J. Different. Geom., 6:4 (1972), 561–576 | MR | Zbl

[11] Nishida T., “A note on a theorem of Nirenberg”, J. Different. Geom., 12:4 (1977), 629–633 | MR | Zbl

[12] Nishida T., Kawashima S., Matsumura A., “On the fluid-dynamical approximation to the Boltzman equation at the level of the Navier–Stokes equation”, Comm. Math. Phys., 70:2 (1979), 97–124 | DOI | MR | Zbl

[13] Nishida T., Matsumura A., “The initial value problem for the equations of motion of viscous and heat-conductive gases”, J. Math. Kyoto Univ., 20:1 (1980), 67–104 | MR | Zbl

[14] Galkin V. A., “Funktsionalnye resheniya zakonov sokhraneniya”, DAN SSSR, 310:4 (1990), 834–839 | MR | Zbl

[15] Leray J., “Etude de diverses équations intégrales nonlineaires et de quelques problèmes que pose l'hydrodinamique”, J. Math. Pures Appl., 12 (1933), 1–82 | MR

[16] Bautin S. P., “Kharakteristicheskaya zadacha Koshi dlya kvazilineinoi analiticheskoi sistemy”, Differents. uravneniya, 12:11 (1976), 2052–2063 | MR | Zbl

[17] Vershinin S. V., Sidorov A. F., “O povedenii reshenii uravnenii dvoinykh voln v okrestnosti oblasti pokoya”, PMM, 39:6 (1975), 1043–1050 | MR | Zbl

[18] Titov S. S., “O nelineinykh uravneniyakh tipa Fuksa”, Dinam. sploshn. sredy, no. 109, Novosibirsk, 1994, 109–122 | MR

[19] Sidorov A. F., “On certain representation of solutions nonlinear initial value problems in gas dynamics”, Archives Mech., 27, Warszawa, 1975, 591–597 | MR | Zbl

[20] Sidorov A. F., “Primenenie spetsialnykh konstruktsii ryadov dlya rascheta osobennostei obobschennykh reshenii nelineinykh uravnenii”, Konstruirov. algoritmov i reshenie zadach matem. fiz., IPM AN SSSR, M., 1987, 79–97

[21] Kokovikhina O. V., Sidorov A. F., “Spetsialnye konstruktsii ryadov dlya resheniya nelineinykh uravnenii s chastnymi proizvodnymi”, Chislen. metody mekhan. sploshn. sredy, 15, No 3, Novosibirsk, 1984, 72–84 | MR | Zbl

[22] Sidorov A. F., Korzunin L. G., Filimonov M. Yu., “Approximate method for solving nonlinear initial boundary problems based on special construction of series”, Soviet J. Numer. Anal. Math. Modelling, 8:2 (1993), 101–126 | MR

[23] Titov S. S., “Razlozhenie reshenii nelineinykh uravnenii v dvoinye ryady”, Differents. uravneniya, 14:10 (1978), 1844–1850 | MR | Zbl

[24] Manin Yu. I., “Algebraicheskie aspekty nelineinykh differentsialnykh uravnenii”, Itogi nauki i tekhn. VINITI. Sovremen. probl. matem., 11, 1978, 5–152 | MR | Zbl

[25] Malgranzh B., Idealy differentsiruemykh funktsii, Mir, M., 1968, 131 pp.

[26] Zhevlakov K. A., Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Mir, M., 1968, 431 pp.

[27] Shestakov I. P., “Algebry Maltseva”, Algebra i logika, 13:2 (1974), 204–213

[28] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978, 339 pp. | MR

[29] Ibragimov N. Kh., Gruppy preobrazovanii v matematicheskoi fizike, Mir, M., 1983, 280 pp. | MR

[30] Zhiber A. V., “Uravneniya $n$-voln i sistema nelineinykh uravnenii Shredingera”, Teor. i matem. fizika, 52:3 (1982), 405–413 | MR | Zbl

[31] Filippov V. T., “Odnorodnye algebry Bola”, Sib. matem. zhurn., 35:4 (1994), 919–926 | MR | Zbl

[32] Maltsev A. I., Algebraicheskie sistemy, Nauka, M., 1970, 392 pp. | MR

[33] Titov S. S., “Ob evolyutsii periodicheskoi teplovoi volny”, Analiticheskie metody i optimizatsiya protsessov zhidkosti i gaza SAMGOP–94, Mezhdunarodn. shkola-seminar, Arzamas–16, 1994, 107–108

[34] Stenli R., Perechislitelnaya kombinatorika, Mir, M., 1990, 440 pp. | MR

[35] Orlov A. G., “Ob asimptotike koeffitsientov Teilora algebraicheskikh funktsii”, Sib. matem. zhurn., 35:5 (1994), 1125–1137 | MR | Zbl

[36] Burbaki N., Spektralnaya teoriya, Mir, M., 1972, 183 pp. | MR | Zbl

[37] Walter W., “An elementary proof of the Cauchy–Kowalevsky theorem”, Amer. Math. Monthly, 92:2 (1985), 115–126 | DOI | MR | Zbl

[38] Ovsyannikov L. V., Analiticheskie gruppy, Izd-vo Novosibirsk. un-ta, Novosibirsk, 1972, 237 pp. | MR

[39] Gantmakher F. R., Teoriya matrits, Nauka, M., 1967, 575 pp. | MR

[40] Sidorov A. F., Shapeev V. P., Yanenko N. N., Metod differentsialnykh svyazei i ego primenenie v gazovoi dinamike, Nauka, Novosibirsk, 1984, 272 pp. | MR