Geodesic
Symmetries, the current function, and exact solutions for Broadwell's two-dimensional stationary kinetic model
Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 3, pp. 350-359 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We investigate the Broadwell stationary kinetic model for four velocities on a plane using the current function that satisfies a partial differential equation. For this equation, we evaluate the algebras of classical and nonclassical symmetries and then construct invariant solutions. All classes of solutions describe nonpotential flows. We consider the relation between nonclassical symmetries and previously obtained solutions.
Keywords: Broadwell kinetic model, current function, symmetry. 
@article{TMF_2014_179_3_a3,
     author = {O. V. Ilyin},
     title = {Symmetries, the~current function, and exact solutions for {Broadwell's} two-dimensional stationary kinetic model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {350--359},
     year = {2014},
     volume = {179},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_179_3_a3/}
}
TY  - JOUR
AU  - O. V. Ilyin
TI  - Symmetries, the current function, and exact solutions for Broadwell's two-dimensional stationary kinetic model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2014
SP  - 350
EP  - 359
VL  - 179
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2014_179_3_a3/
LA  - ru
ID  - TMF_2014_179_3_a3
ER  - 
%0 Journal Article
%A O. V. Ilyin
%T Symmetries, the current function, and exact solutions for Broadwell's two-dimensional stationary kinetic model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2014
%P 350-359
%V 179
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2014_179_3_a3/
%G ru
%F TMF_2014_179_3_a3
O. V. Ilyin. Symmetries, the current function, and exact solutions for Broadwell's two-dimensional stationary kinetic model. Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 3, pp. 350-359. http://geodesic.mathdoc.fr/item/TMF_2014_179_3_a3/

[1] S. K. Godunov, U. M. Sultangazin, UMN, 26:3(159) (1971), 3–51 | DOI | MR | Zbl

[2] A. V. Bobylev, G. Spiga, J. Phys. A, 27:22 (1994), 7451–7459 | DOI | MR | Zbl

[3] A. V. Bobylev, G. Caraffini, G. Spiga, Eur. J. Mech. B/Fluids, 19:2 (2000), 303–315 | DOI | MR | Zbl

[4] A. V. Bobylev, Math. Methods Appl. Sci., 19:10 (1996), 825–845 | 3.0.CO;2-1 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[5] O. Ilyin, J. Stat. Phys., 146:1 (2012), 67–72 | DOI | MR | Zbl

[6] O. Lindblom, N. Eiler, TMF, 131:2 (2002), 179–193 | DOI | DOI | MR | Zbl

[7] O. V. Ilin, TMF, 170:3 (2012), 481–488 | DOI | DOI

[8] H. Cabannes, Eur. J. Mech. B/Fluids, 16:1 (1997), 1–15 | MR | Zbl

[9] V. V. Zharinov, Lecture Notes on Geometrical Aspects of Partial Differential Equations, Series on Soviet and East European Mathematics, 9, World Sci., Singapore, 1992 | MR | Zbl

[10] N. H. Ibragimov, Transformation Groups Applied to Mathematical Physics, Reidel, Dordrecht, 1985 | MR | Zbl

[11] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | DOI | MR | Zbl

[12] I. S. Krasil'shchik, P. H. M. Kersten, Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations, Mathematics and its Applications, 507, Kluwer, Dordrecht, 2000 | MR | Zbl

[13] C. Cercignani, R. Illner, M. Shinbrot, Commun. Math. Phys., 114:4 (1988), 687–698 | DOI | MR | Zbl

[14] P. J. Olver, Appl. Numer. Math., 10:3–4 (1992), 307–324 | DOI | MR | Zbl

[15] P. J. Olver, E. M. Vorob'ev, “Nonclassical and conditional symmetries”, CRC Handbook of Lie Group Analysis of Differential Equations, v. 3, New Trends in Theoretical Developments and Computational Methods, ed. N. H. Ibragimov, CRC Press, Boca Raton, FL, 1996, 291–328 | MR | Zbl

[16] P. J. Olver, P. Rosenau, SIAM J. Appl. Math., 47:2 (1987), 263–278 | DOI | MR | Zbl

[17] P. A. Clarkson, M. D. Kruskal, J. Math. Phys., 30:10 (1989), 2201–2213 | DOI | MR | Zbl