Geodesic
On one problem in physical kinetics
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 2061-2069 
S. M. Andriyan; A. Kh. Khachatryan. On one problem in physical kinetics. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 2061-2069. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a13/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The temperature-jump problem in physical kinetics with accommodation is considered. The problem is reduced to a symmetric system of integral equations with a total-difference kernel on a half-line. The existence of a solution to the obtained system is proved by applying a special factorization. An analytical solution to the system of integral equations is proposed, and its asymptotic behavior is investigated.

[1] Loyalka S. K., “Momentum and temperature slip coefficients with arbitrary accomodation at the surface”, J. Chem. Phys., 48 (1968), 5432–5436 | DOI

[2] Loyalka S. K., Siewert C. E., Thomas J. R., “Temperature jump problem with arbitrary accomodation”, Phys. Fluids, 21:5 (1978), 854–855 | DOI | Zbl

[3] Latyshev A. V., Yushkanov A. A., “Primenenie metoda Keiza k resheniyu linearizovannogo kineticheskogo BGK uravneniya v zadache o temperaturnom skachke”, Prikl. matem. i mekhan., 54:4 (1990), 581–596 | MR

[4] Latyshev A. V., Yushkanov A. A., “Analiticheskoe reshenie modelnogo BGK-uravneniya Boltsmana v zadache o temperaturnom skachke s uchetom akkomodatsii energii”, Matem. modelirovanie, 4:10 (1992), 61–66 | MR

[5] Barichello L. B., Siewert C. E., “The temperature-jump problem in rarefied-gas dynamics”, European J. Appl. Math., 11:4 (2000), 353–364 | DOI | MR

[6] Engibaryan N. B., Engibaryan B. H., “O metode sdviga albedo”, Astrofizika, 38:3 (1995), 417–431 | MR

[7] Engibaryan N. B., Engibaryan B. N., “Integralnoe uravnenie svertki na polupryamoi s vpolne monotonnym yadrom”, Matem. sb., 187:10 (1996), 53–72 | MR | Zbl

[8] Ivanov V. V., Rybicki G. B., Kasaurov A. M., Albedo shifting, Preprint Series No 3478, Smithsonian Center for Astrophys, Harvard, 1992

[9] Gokhberg I. Ts., Krein M. D., “Sistemy integralnykh uravnenii na polupryamoi s yadrami, zavisyaschimi ot raznosti argumentov”, Uspekhi matem. nauk, 13:2 (1968), 3–72 | MR

[10] Arabadzhyan L. G., Engibaryan N. B., “Uravnenie v svertkakh i nelineinye funktsionalnye uravneniya”, Matem. analiz. Itogi nauki i tekhn., 22, VINITI AN SSSR, M., 1984, 175–244 | MR

[11] Engibaryan N. B., “Faktorizatsiya matrits-funktsii i nelineinye integralnye uravneniya”, Izv. AN ArmSSR. Matematika, 15:3 (1980), 233–244 | MR

[12] Bellman R., Kuk K., Differentsialno-raznostnye uravneniya, Mir, M., 1967 | MR | Zbl

[13] Engibaryan N. B., Khachatryan A. Kh., “O nekotorykh integralnykh uravneniyakh tipa svertki v kineticheskoi teorii”, Zh. vychisl. matem. i matem. fiz., 38:3 (1998), 466–482 | MR | Zbl

[14] Khachatryan Kh. A., “Primenenie metoda sdviga albedo k resheniyu konservativnogo integralnogo uravneniya s summarno-raznostnym yadrom”, Zh. vychisl. matem. i matem. fiz., 42:6 (2002), 905–912 | MR | Zbl