Geodesic
Existence and stability analysis for the Carleman kinetic system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 2076-2087 Cet article a éte moissonné depuis la source Math-Net.Ru

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A global existence theorem for the discrete Carleman system in the Sobolev class $W^{1,2}$ is proved by the Leray–Schauder topological degree method, which was not previously applied to discrete kinetic equations. The instability of the nonequilibrium steady flow on a bounded interval is established in the linear approximation. 
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     title = {Existence and stability analysis for the {Carleman} kinetic system},
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O. V. Ilyin. Existence and stability analysis for the Carleman kinetic system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 2076-2087. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a8/

[1] Sultangazin U. M., Diskretnye nelineinye modeli uravneniya Boltsmana, Nauka, Alma-Ata, 1985 | MR

[2] Monaco R., Preziosi L., Fluid dynamic applications of the discrete Boltzmann equation, Ser. Advances Math. Appl. Sci., 3, World Scient. Publ. Co. Pte. Ltd., Singapore, 1991 | MR

[3] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR

[4] Vedenyapin V. V., “Differentsialnye formy v prostranstvakh bez normy. Teorema edinstvennosti $H$-funktsii Boltsmana”, Uspekhi matem. nauk, 43:1 (1988), 159–179 | MR | Zbl

[5] Dubrovin B. A., Novikov S. P., Fomenko A., Sovremennaya geometriya, v. 2, Geometriya i topologiya mnogoobrazii, Editorial, Kiev, 2001

[6] Sattinger D. H., Topics in stability and bifurcation theory, Lect. Notes Math., 309, Springer, Berlin etc., 1972 | MR

[7] Adams R. A., Sobolev spaces, Acad. Press, New York, 1975 | MR | Zbl

[8] Krasnoselskii M. A., Topologicheskie metody v teorii nelineinykh integralnykh uravnenii, Gostekhteorizdat, M., 1956 | MR

[9] Nirenberg L., Lektsii po nelineinomu funktsionalnomu analizu, Mir, M., 1977 | MR | Zbl

[10] Bobylev A. V., Tochnye i priblizhennye metody v teorii nelineinykh kineticheskikh uravnenii Boltsmana i Landau, IPMatem. AN SSSR, M., 1987 | MR

[11] Hartman P., Ordinary differential equations, Sec. ed., Wiley, New York, 1973 | MR

[12] Ains E. L., Obyknovennye differentsialnye uravneniya, Gos. NKTP nauchno-tekhn. lit., Kharkov, 1939

[13] Aristov V. V., “Resheniya uravneniya Boltsmana pri malykh chislakh Knudsena”, Zh. vychisl. matem. i matem. fiz., 44:6 (2004), 1127–1140 | MR | Zbl

[14] Cherchinyani K., Teoriya i prilozheniya uravneniya Boltsmana, Mir, M., 1978 | MR

[15] Kogan M. N., Dinamika razrezhennogo gaza, Nauka, M., 1967