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@article{LKN_2010_a0, author = {A. G. Kulikovskii and E. I. Sveshnikova and A. P. Chugainova}, title = {Mathematical methods for studying discontinuous solutions of nonlinear hyperbolic systems of equations}, journal = {Lekcionnye kursy NOC}, pages = {3--120}, publisher = {mathdoc}, year = {2010}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/LKN_2010_a0/} }
TY - JOUR AU - A. G. Kulikovskii AU - E. I. Sveshnikova AU - A. P. Chugainova TI - Mathematical methods for studying discontinuous solutions of nonlinear hyperbolic systems of equations JO - Lekcionnye kursy NOC PY - 2010 SP - 3 EP - 120 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/LKN_2010_a0/ LA - ru ID - LKN_2010_a0 ER -
%0 Journal Article %A A. G. Kulikovskii %A E. I. Sveshnikova %A A. P. Chugainova %T Mathematical methods for studying discontinuous solutions of nonlinear hyperbolic systems of equations %J Lekcionnye kursy NOC %D 2010 %P 3-120 %I mathdoc %U http://geodesic.mathdoc.fr/item/LKN_2010_a0/ %G ru %F LKN_2010_a0
A. G. Kulikovskii; E. I. Sveshnikova; A. P. Chugainova. Mathematical methods for studying discontinuous solutions of nonlinear hyperbolic systems of equations. Lekcionnye kursy NOC, Mathematical methods for studying discontinuous solutions of nonlinear hyperbolic systems of equations (2010), pp. 3-120. http://geodesic.mathdoc.fr/item/LKN_2010_a0/
[1] Bakholdin I. B., Bezdissipativnye razryvy v mekhanike sploshnoi sredy, Fizmatlit, M., 2004
[2] Barmin A. A., Kulikovskii A. G., “Fronty ionizatsii i rekombinatsii v elektromagnitnom pole”, Itogi nauki. Gidromekhanika, 5, Nauka, M., 1971, 5–31
[3] Barmin A. A., Uspenskii V. S., “Razvitie pulsatsionnykh rezhimov v odnomernykh nestatsionarnykh MGD-techeniyakh s vyklyucheniem elektroprovodnosti”, Izv. AN SSSR. MZhG, 14:4 (1986), 115–122
[4] Vvedenskaya N. D., “Primer needinstvennosti obobschennogo resheniya kvazilineinoi sistemy uravnenii”, DAN SSSR, 136:3 (1961), 532–533 | MR | Zbl
[5] Galin G. Ya., “Ob udarnykh volnakh v sredakh s proizvolnym uravnenie sostoyaniya”, DAN SSSR, 119:6 (1958), 1106–1109 | MR | Zbl
[6] Galin G. Ya., “K teorii udarnykh voln”, DAN SSSR, 127:1 (1959), 55–58 | MR | Zbl
[7] Gelfand I. M., “Nekotorye zadachi teorii kvazilineinykh uravnenii”, UMN, 14:2 (86) (1959), 87–158 | MR | Zbl
[8] Godunov S. K., “O ponyatii obobschennogo resheniya”, DAN SSSR, 134:6 (1960), 1279–1282 | MR | Zbl
[9] Godunov S. K., “Interesnyi klass kvazilineinykh sistem”, DAN SSSR, 139:3 (1961), 521–523 | MR | Zbl
[10] Godunov S. K., “O needinstvennosti “razmazyvaniya” razryvov v resheniyakh kvazilineinykh sistem”, DAN SSSR, 136:2 (1961), 272–273 | MR | Zbl
[11] Godunov S. K., “Problema obobschennogo resheniya v teorii kvazilineinykh uravnenii i v gazovoi dinamike”, UMN, 17:3 (105) (1962), 147–158 | MR | Zbl
[12] Godunov S. K., Uravneniya matematicheskoi fiziki, Fizmatlit, M., 1971, 416 pp. | MR | Zbl
[13] Godunov S. K., Romenskii E. I., Elementy mekhaniki sploshnykh sred i zakony sokhraneniya, Universitetskaya seriya, 4, Nauchnaya kniga, Novosibirsk, 1998, 267 pp. | MR | Zbl
[14] De Groot S. R., Mazur P., Neravnovesnaya termodinamika, Mir, M., 1964, 456 pp.
[15] Dyachenko V. F., “O zadache Koshi dlya kvazilineinykh sistem”, DAN SSSR, 136:1 (1961), 16–17 | Zbl
[16] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov. Metod obratnoi zadachi, Nauka, M., 1980 | MR | Zbl
[17] Zhermen P., Kurs mekhaniki sploshnykh sred, Vysshaya shkola, M., 1983, 400 pp.
[18] Zeldovich Ya. B., Barenblatt G. I., Librovich V. B., Makhviladze G. M., Matematicheskaya teoriya goreniya i vzryva, Nauka, M., 1980 | MR
[19] Ilichev A. T., Uedinennye volny v modelyakh gidromekhaniki, Fizmatlit, M., 2003, 256 pp.
[20] Kalashnikov A. S., “Postroenie obobschennykh reshenii kvazilineinykh uravnenii pervogo poryadka bez usloviya vypuklosti kak predelov reshenii parabolicheskikh uravnenii s malym parametrom”, DAN SSSR, 127:1 (1959), 27–30 | MR | Zbl
[21] Karpman V. I., Nelineinye volny v dispergiruyuschikh sredakh, Nauka, M., 1973, 175 pp. | MR
[22] Kruzhkov S. N., Trudy S. N. Kruzhkova, eds. Bakhvalov N. S., Galkin V. A., Dubinskii Yu. A., Fizmatlit, M., 2000, 334 pp. | MR | Zbl
[23] Kulikovskii A. G., “O strukture udarnykh voln”, PMM, 26:4 (1962), 631–641 | MR | Zbl
[24] Kulikovskii A. G., “O poverkhnostyakh razryva, razdelyayuschikh idealnye sredy s razlichnymi svoistvami. Volny rekombinatsii”, PMM, 32:6 (1968), 1125–1131 | Zbl
[25] Kulikovskii A. G., “O svoistvakh udarnykh adiabat v okrestnosti tochek Zhuge”, Izvestiya AN SSSR. MZhG, 14:2 (1979), 317–319
[26] Kulikovskii A. G., “O vozmozhnom vliyanii kolebanii v strukture razryva na mnozhestvo dopustimykh razryvov”, DAN SSSR, 275:6 (1984), 1349–1352 | MR
[27] Kulikovskii A. G., “Silnye razryvy v techeniyakh sploshnykh sred i ikh struktura”, Teoriya veroyatnostei, teoriya funktsii, mekhanika, Tr. MIAN SSSR, 182, Nauka, M., 1988, 261–291 | MR | Zbl
[28] Kulikovskii A. G., Lyubimov G. A., Magnitnaya gidrodinamika, Fizmatgiz, M., 1962, 246 pp. | Zbl
[29] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001, 608 pp. | MR | Zbl
[30] Kulikovskii A. G., Sveshnikova E. I., “Avtomodelnaya zadacha o deistvii vnezapnoi nagruzki na granitsu uprugogo poluprostranstva”, PMM, 49:2 (1985), 284–291 | MR | Zbl
[31] Kulikovskii A. G., Sveshnikova E. I., “O raspade proizvolnogo nachalnogo razryva v uprugoi srede”, PMM, 52:6 (1988), 1007–1012 | MR | Zbl
[32] Kulikovskii A. G., Sveshnikova E. I., Nelineinye volny v uprugikh sredakh, Mosk. litsei, M., 1998, 412 pp.
[33] Kulikovskii A. G., Sveshnikova E. I., “Priznak nesuschestvovaniya ili needinstvennosti reshenii avtomodelnykh zadach”, PMM, 65:6 (2001), 971–982 | MR | Zbl
[34] Kulikovskii A. G., Chugainova A. P., “Ob usloviyakh raspada nelineinoi volny v vyazkouprugoi srede”, ZhVM i MF, 38:2 (1998), 315–323 | MR | Zbl
[35] Kulikovskii A. G., Chugainova A. P., “Modelirovanie vliyaniya melkomasshtabnykh dispersionnykh protsessov v sploshnoi srede na formirovanie krupnomasshtabnykh yavlenii”, ZhVM i MF, 44:6 (2004), 1119–1126 | MR | Zbl
[36] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1964, 830 pp. | MR | Zbl
[37] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Fizmatgiz, M., 1958, 678 pp. | MR | Zbl
[38] Landau L. V., Lifshits E. M., Teoreticheskaya fizika, v. 6, Gidrodinamika, Nauka, M., 1986, 736 pp. | MR | Zbl
[39] Levin V. A., Markov V. V., Zhuravskaya T. A, Osinkin S. F., “Nelineinye volnovye protsessy pri initsiirovanii i rasprostranenii gazovoi detonatsii”, Nelineinaya dinamika, Tr. MIAN, 251, Nauka, M., 2005, 200–214 | MR | Zbl
[40] Lyubarskii G. Ya., “O strukture udarnykh voln”, PMM, 25:6 (1961), 1041–1049 | MR | Zbl
[41] Lyubarskii G. Ya., “O suschestvovanii udarnykh voln maloi intensivnosti”, PMM, 26:3 (1962), 511–519 | MR | Zbl
[42] Lyapidevskii V. Yu., Teshukov V. M., Matematicheskie modeli rasprostraneniya dlinnykh voln v neodnorodnoi zhidkosti, Izd-vo Sib. otd-niya RAN, Novosibirsk, 2000, 419 pp.
[43] Oleinik O. A., “O postroenii obobschennogo resheniya zadachi Koshi dlya kvazilineinogo uravneniya pervogo poryadka putem vvedeniya “ischezayuschei vyazkosti””, UMN, 14:2 (86) (1959), 159–164 | MR | Zbl
[44] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1978, 687 pp. | MR | Zbl
[45] Sedov L. I., Mekhanika sploshnoi sredy, v. 1, 2, Nauka, M., 1994, t. 1: 528 s., t. 2: 560 pp. | MR | Zbl
[46] Sedov L. I., Korobeinikov V. P., Markov V. V., “Teoriya rasprostraneniya vzryvnykh voln”, Teoreticheskaya i matematicheskaya fizika, Tr. MIAN SSSR, 175, Nauka, M., 1986, 178–216 | MR | Zbl
[47] Sobolev S. L., “O smeshannoi zadache dlya uravnenii v chastnykh proizvodnykh s dvumya nezavisimymi peremennymi”, DAN SSSR, 122:4 (1958), 555–558 | MR | Zbl
[48] Chugainova A. P., “O formirovanii avtomodelnogo resheniya v zadache o nelineinykh volnakh v uprugom poluprostranstve”, PMM, 52:4 (1988), 692–697 | MR
[49] Uizem Dzh. B., Lineinye i nelineinye volny, Mir, M., 1977, 622 pp. | MR | Zbl
[50] Butler D. S., “One-dimensional flow in an ionizing gas”, J. Fluid Mech., 23 (1965), 1–21 | DOI | MR | Zbl
[51] Germain P., Contribution à la théorie des ondes de choc en magnétodynamique des fluides, Publ. 97, Office National d'Etudes et de Recherches Aeronautiques, Paris, 1959 | MR
[52] Germain P., Cours de Mécanique des Milieux Continus, v. 1, Théorie Générale, Masson et Cie, Éditeurs, Paris, 1973 | MR | Zbl
[53] Gordon P., “Paths connecting elementary critical points of dynamical systems”, SIAM J. Appl. Math., 26:1 (1974), 35–102 | DOI | MR | Zbl
[54] Hanyga A., On the solution to the Riemann problem for arbitrary hyperbolic system of conservation laws, Publications of Institute of Geophysics, No. A-1(98), PWN, Warszawa, 1976
[55] Hersh R., “Boundary conditions for equations of evolution”, Arch. Rational Mech. Anal., 16:4 (1964), 243–264 | MR | Zbl
[56] Kulikovskii A., Sveshnikova E., Nonlinear Waves in Elastic Media, CRC Press, Boca Raton, FL, 1995, x+237 pp. | MR | Zbl
[57] Lax P. D., “Hyperbolic systems of conservation laws. II”, Comm. Pure Appl. Math., 10:4 (1957), 537–566 | DOI | MR | Zbl
[58] Smoller J., Shock Waves and Reaction-Diffusion Equations, Grundlehren Math. Wiss., 258, Springer-Verlag, New York, 1983, xxi+581 pp. | MR | Zbl