Geodesic
Solutions of Discrete-Velocity Boltzmann Equations via Bateman and Riccati Equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 179-193 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We propose several approaches for solving two discrete-velocity Boltzmann equations using the rescaling ansatz and the truncated Painlev'e expansions. We use solutions of the two- and three-dimensional Bateman equations for the singularity manifold conditions to reduce the problem to Riccati equations. Both equations fail the Painlevé test. 
@article{TMF_2002_131_2_a0,
     author = {O. Lindblom and N. Euler},
     title = {Solutions of {Discrete-Velocity} {Boltzmann} {Equations} via {Bateman} and {Riccati} {Equations}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--193},
     year = {2002},
     volume = {131},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a0/}
}
TY  - JOUR
AU  - O. Lindblom
AU  - N. Euler
TI  - Solutions of Discrete-Velocity Boltzmann Equations via Bateman and Riccati Equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2002
SP  - 179
EP  - 193
VL  - 131
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a0/
LA  - ru
ID  - TMF_2002_131_2_a0
ER  - 
%0 Journal Article
%A O. Lindblom
%A N. Euler
%T Solutions of Discrete-Velocity Boltzmann Equations via Bateman and Riccati Equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2002
%P 179-193
%V 131
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a0/
%G ru
%F TMF_2002_131_2_a0
O. Lindblom; N. Euler. Solutions of Discrete-Velocity Boltzmann Equations via Bateman and Riccati Equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 179-193. http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a0/

[1] J. Weiss, M. Tabor, G. Carnevale, J. Math. Phys., 24 (1983), 522–526 | DOI | MR | Zbl

[2] W.-H. Steeb, N. Euler, Nonlinear Evolution Equations and the Painlevé Test, World Scientific, Singapore, 1988 | MR

[3] F. Cariello, M. Tabor, Physica D, 39 (1989), 77–94 | DOI | MR | Zbl

[4] N. Euler, O. Lindblom, Int. J. Diff. Equat. Appl., 1 (2000), 205–222 | MR | Zbl

[5] S. L. Godunov, U. M. Sultangazin, UMN, 26:3 (1971), 3–51 | MR | Zbl

[6] H. Cabannes, “Survey on exact solutions for discrete models of the Boltzmann equation”, Computational Fluid Dynamics, eds. D. Leutloff, R. C. Srivastava, Springer, Berlin, 1994, 103–114 | MR

[7] F. Cariello, M. Tabor, Physica D, 53 (1991), 59–70 | DOI | MR | Zbl