A boundary value problem for the two dimensional Broadwell model

Carlo Cercignani; Reinhard Illner; Marvin Shinbrot

doi:10.1007/bf01229460

journal article Dec 01, 1988

A boundary value problem for the two dimensional Broadwell model

Carlo Cercignani Reinhard Illner Marvin Shinbrot

Communications in Mathematical Physics Vol. 114 No. 4 pp. 687-698 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf01229460

Topics

No keywords indexed for this article. Browse by subject →

References

19

[1]

Arthur, M.D., Cercignani, C.: Nonexistence of a steady rarefied supersonic flow in a half-space. Z. Angew. Math. Phys.31, 634 (1980) 10.1007/bf01596163

[2]

Bardos, C., Caflisch, R.E., Nicolaenko, B.: The Milne and Kramers problems for the Boltzmann equation of a hard sphere gas. Commun. Pure Appl. Math.39, 322 (1986) 10.1002/cpa.3160390304

[3]

Beale, J.T.: Large-time behavior of the Broadwell model of a discrete velocity gas. Commun. Math. Phys.102, 217?235 (1985) 10.1007/bf01229378

[4]

Beals, R.: An abstract treatment of some forward-backward problems of transport and scattering. J. Funct. Anal.34, 1 (1979) 10.1016/0022-1236(79)90021-1

[5]

Cercignani, C.: Mathematical methods in kinetic theory. New York: Plenum Press 1969 10.1007/978-1-4899-5409-1

[6]

Cercignani, C.: Theory and application of the Boltzmann equation. New York: Elsevier 1975

[7]

Cercignani, C.: Elementary solutions of the linearized gas dynamics Boltzmann equation and their application to the slip flow problem. Ann. Phys. (NY)20, 219 (1962) 10.1016/0003-4916(62)90199-9

[8]

Cercignani, C.: Existence and uniqueness in the large for boundary value problems in kinetic theory. J. Math. Phys.8, 1653?1656 (1967) 10.1063/1.1705405

[9]

Cercignani, C.: On the general solution of the steady linearized Boltzmann equation. In: Rarefied gas dynamics. Becker, M., Fiebig, M. (eds.). Porz-Wahn: DFVLR Press 1974

[10]

Cercignani, C.: Half-space problems in the kinetic theory of gases. In: Trends in applications of pure mathematics to mechanics. Kröner, E., Kirchgässer, K. (eds.), Lecture Notes in Physics, Vol. 249, p. 35. Berlin, Heidelberg, New York: Springer 1986 10.1007/bfb0016381

[11]

Cercignani, C., Illner, R., Shinbrot, M.: A boundary value problem for discrete velocity models. Duke Math. J. (to appear) 10.1215/s0012-7094-87-05543-8

[12]

Cercignani, C., Illner, R., Pulvirenti, M., Shinbrot, M.: On nonlinear stationary half-space problems in discrete kinetic theory (to appear)

[13]

Gatignol, R.: Théorie Cinétique des gaz a répartition discréte des vitésses. Lecture Notes in Physics, Vol. 36. Berlin, Heidelberg, New York: Springer 1975

[14]

Greenberg, W., van der Mee, C.: An abstract approach to evaporation models in rarefied gas dynamics. Z. Angew. Math. Phys.35, 166 (1984) 10.1007/bf00947929

[15]

Illner, R.: Global existence results for discrete velocity models of the Boltzmann equation in several dimensions. J.Méc. Théor. Appl.1, 611?622 (1982)

[16]

Illner, R.: Examples of non-bounded solutions in discrete kinetic theory. J. Méc. Théor. Appl.5, 561?571 (1986)

[17]

Kaniel, S., Shinbrot, M.: The Boltzmann equation. I. Uniqueness and local existence. Commun. Math. Phys.58, 65?84 (1978) 10.1007/bf01624788

[18]

Schaefer, H.: Über die Methode der a priori Schranken. Math. Ann.129, 415?416 (1955) 10.1007/bf01362380

[19]

Smart, D.R.: Fixed point theorems. New York: Cambridge University Press 1974

Metrics

18

Citations

19

References

Details

Published: Dec 01, 1988
Vol/Issue: 114(4)
Pages: 687-698
License: View

Authors

Cite This Article

Carlo Cercignani, Reinhard Illner, Marvin Shinbrot (1988). A boundary value problem for the two dimensional Broadwell model. Communications in Mathematical Physics, 114(4), 687-698. https://doi.org/10.1007/bf01229460

A boundary value problem for the two dimensional Broadwell model

You May Also Like