Geodesic
Asymptotics of the solution to the point explosion problem in the case of cylindrical symmetry
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 7, pp. 1207-1222 
I. M. Troyanova; V. A. Tupchiev. Asymptotics of the solution to the point explosion problem in the case of cylindrical symmetry. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 7, pp. 1207-1222. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a7/
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     title = {Asymptotics of the solution to the point explosion problem in the case of cylindrical symmetry},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the problem of a strong point explosion with cylindrical symmetry, high-order asymptotic expansions of the solution with respect to the viscosity and thermal conductivity are constructed and justified.

[1] Rozhdestvenskii B. L., Yanenko H. N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya v gazovoi dinamike, Nauka, M., 1978

[2] Lifshits E. M., Pitaevskii L. P., Fizicheskaya kinetika, Nauka, M., 1979 | MR | Zbl

[3] Sedov L. I., Metod podobiya i razmernosti v mekhanike, Nauka, M., 1987 | MR

[4] Korobeinikov V. P., Zadachi teorii tochechnogo vzryva, Nauka, M., 1985 | MR

[5] Volosevich P. P., Livanov E. I., Avtomodelnye resheniya zadach gazovoi dinamiki i teploperenosa, Nauka, M., 1997

[6] Krasheninnikova N. L., “O neustanovivshemsya dvizhenii gaza, vytesnyaemogo porshnem”, Izv. AN SSSR. Otd. tekhn. nauk, 1955, no. 8

[7] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Nauka, M., 1973 | MR

[8] Tupchiev V. A., “Asimptotika resheniya kraevoi zadachi dlya sistemy differentsialnykh uravnenii pervogo poryadka s malym parametrom pri proizvodnoi”, Dokl. AN SSSR, 143:6 (1962), 1296–1299

[9] Tupchiev V. A., “Ob uglovykh resheniyakh kraevykh zadach s malym parametrom pri proizvodnoi v sisteme uravnenii pervogo poryadka”, Vestn. MGU. Matem., mekhan., 1963, no. 3, 17–24

[10] Hoppenstead F., “Singular perturbations on infinite interval”, Trans. Amer. Math. Soc., 123:2 (1966), 521–535 | DOI | MR | Zbl