Uniqueness of self-similar solutions to the Riemann problem for the Hopf equation with complex nonlinearity
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1363-1370 Cet article a éte moissonné depuis la source Math-Net.Ru

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Solutions of the Riemann problem for a generalized Hopf equation are studied. The solutions are constructed using a sequence of non-overturning Riemann waves and shock waves with stable stationary and nonstationary structures.
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A. G. Kulikovskii; A. P. Chugainova; V. A. Shargatov. Uniqueness of self-similar solutions to the Riemann problem for the Hopf equation with complex nonlinearity. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1363-1370. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a13/

[1] Kulikovskii A. G., “O vozmozhnom vliyanii kolebanii v strukture razryva na mnozhestvo dopustimykh razryvov”, Dokl. AN SSSR, 275:6 (1984), 1349–1352 | MR

[2] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2012

[3] Kulikovskii A. G., Chugainova A. P., “Modelirovanie vliyaniya melkomasshtabnykh dispersionnykh protsessov v sploshnoi srede na formirovanie krupnomasshtabnykh yavlenii”, Zh. vychisl. matem. matem. fiz., 44:6 (2004), 1119–1126 | MR | Zbl

[4] Kulikovskii A. G., Chugainova A. P., “Klassicheskie i neklassicheskie razryvy v resheniyakh uravnenii nelineinoi teorii uprugosti”, Uspekhi matem. nauk, 380:63.2 (2008), 85–152 | DOI | MR

[5] Chugainova A. P., “Nestatsionarnye resheniya obobschennogo uravneniya Kortevega–de Vriza–Byurgersa”, Tr. MIAN, 281, MAIK, M., 2013, 215–223 | Zbl

[6] Chugainova A. P., Shargatov V. A., “Ustoichivost nestatsionarnykh reshenii obobschennogo uravneniya Kortevega–de Briza–Byurgersa”, Zh. vychisl. matem. i matem. fiz., 55:2 (2015), 251–263 | MR | Zbl

[7] Ilichev A. T., Chugainova A. P., Shargatov V. A., “Spektralnaya ustoichivost osobykh razryvov”, Dokl. AN. Matem., 462:5 (2015), 512–516 | DOI | Zbl

[8] Chugainova A. P., Shargatov V. A., “Ustoichivost struktury razryvov, opisyvaemykh obobschennym uravneniem Kortevega–de Vriza–Byurgersa”, Zh. vychisl. matem. i matem. fiz., 56:2 (2016), 259–274 | DOI | MR | Zbl

[9] Levin V. A., Markov V. V., Osinkin S. F., “Modelirovanie initsiirovaniya detonatsii v goryuchei smesi gazov elektricheskim razryadom”, Khim. fiz., 3:4 (1984), 611–613

[10] Levin V. A., Markov V. V., Osinkin S. F., “Vosstanovlenie detonatsii s pomoschyu razrushayuscheisya obolochki”, Dokl. AN, 352:1 (1997), 333–335

[11] Landau L. D., Lifshits E. M., Gidrodinamika, Nauka. Glavnaya redaktsiya fiziko-matematicheskoi literatury, M., 1986, 736 pp.

[12] Konyukhov A. V., Likhachev A. P., Oparin A. M., Anisimov S. I., Fortov V. E., “Numerical modeling of shock-wave instability in termodynamically nonideal media”, J. Experimental Phys., 98:4 (2004), 811–819

[13] Oleinik O. A., “O edinstvennosti i ustoichivosti obobschennogo resheniya zadachi Koshi dlya kvazilineinogo uravneniya”, Uspekhi matem. nauk, 14:2(86) (1959), 159–164 | MR

[14] Kulikovskii A. G., “O poverkhnostyakh razryva, razdelyayuschikh idealnye sredy s razlichnymi svoistvami: Volny rekombinatsii”, Prikl. matem. i mekhan., 32:6 (1968), 1125–1131 | Zbl