Stability of stationary solutions to the half-space problem for the discrete boltzmann equation with multiple collisions

Kyushu Journal of Mathematics

Volumn 54, Issue 2, 2000, Pages 233-255

  Nikkuni, Yoshiko ^a   Kawashima, Shuichi ^a  

^a KYUSHU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85014762897     PISSN: 13406116     EISSN: None     Source Type: Journal    
DOI: 10.2206/kyushujm.54.233     Document Type: Article

References (17)

1. H. Cabannes. The discrete Boltzmann equation (Theory and applications) (Lecture Notes). University of California, Berkeley, 1980
2. C. Cercignani, R. Illner, M. Pulvienti and M. Shinbrot. On nonlinear stationary half-space problems in discrete kinetic theory. J. Statist. Phys. 54 (1988), 885-896
3. R. Gatignol, Théorie Cinétique de Gaz à Répartition Discrète de Vitesses (Lecture Notes in Physics, 36). Springer, New York, 1975
4. S. Kawashima. Global existence and stability of solutions for discrete velocity models of the Boltzmann equation. Recent Topics in Nonlinear PDE (Lecture Notes in Numer. Appl. Anal., 6). Kinokuniya, Tokyo, 1983, pp.59-85
5. S. Kawashima. Large-time behavior of solutions of the discrete Boltzmann equation. Comm. Math. Phys. 109 (1987), 563-589
6. S. Kawashima. Global solutions to the initial-boundary value problems for the discrete Boltzmann equation. Nonlinear Anal. 17 (1991), 577-597
7. S. Kawashima. Existence and stability of stationary solutions to the discrete Boltzmann equation. Japan J. Indust. Appl. Math. 8 (1991), 389-429
8. S. Kawashima. Large-time behavior of solutions to the discrete Boltzmann equation in the half-space. Transport Theor. Stat. Phys. 21 (1992), 451-463
9. S. Kawashima. Exponential stability of stationary solutions to the discrete Boltzmann equation in a bounded domain. Math. Models Meth. Appl. Sci. 2 (1992), 239-248
10. S. Kawashima and N. Bellomo. The discrete Boltzmann equation with multiple collisions: global existence and stability for the initial value problem. J. Math. Phys. 31 (1990), 245-253
11. S. Kawashima and S. Nishibata. Existence of a stationary wave for the discrete Boltzmann equation in the half-space. Comm. Math. Phys. 207 (1999), 385-409
12. A. Matsumura. Asymptotics toward rarefaction wave for solutions of the Broadwell model of a discrete velocity gas. Japan J. Appl. Math. 4 (1987), 489-502
13. Y. Nikkuni. Stability of stationary solutions to the discrete Boltzmann equation with general boundary conditions. In preparation
14. Y. Nikkuni. Stability of stationary solutions to some discrete velocity model of the Boltzmann equation in the half-space. Funkcial. Ekvac. 42 (1999), 413-434
15. Y. Nikkuni and R. Sakamoto. Solutions to the discrete Boltzmann equation with general boundary conditions. J. Math. Soc. Japan 51 (1999), 757-779
16. Y. Shizuta and S. Kawashima. Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation. Hokkaido Math. J. 14 (1985), 249-275
17. S. Ukai, On the half-space problem for the discrete velocity model of the Boltzmann equation. Advances in Nonlinear Partial Differential Equations and Stochastics. Eds S. Kawashima and T. Yanagisawa, World Scientific, 1998, 160-174