On shock wave solutions for discrete velocity models of the Boltzmann equation

Transport Theory and Statistical Physics

Volumn 27, Issue 1, 1998, Pages 35-66

  Bose, C ^a   Illner, R ^a   Ukai, S ^b  

^a UNIVERSITY OF VICTORIA   (Canada)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032342420     PISSN: 00411450     EISSN: None     Source Type: Journal    
DOI: 10.1080/00411459808205140     Document Type: Article

References (8)

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2. [CN] R.E. Caflisch, B. Nicolaenko, Shock profile solutions of the Boltzmann equation, Commun. Math. Phys. 86, 161-194 (1982)
3. [Co] H. Cornille, Positive 2+1 dimensional exact shock waves solutions to the Broadwell model, J. Math. Phys. 30 (4), 789-797 (1989)
4. [CoP] H. Cornille, and T. Platkowski, Riccati-coupled similarity shock wave solutions for multispeed discrete Boltzmann models, J. Stat. Phys. 71 (3/4), 719-740 (1993)
5. [G] R. Gatignol, Théorie cinétique de gas a repartition discrète de vitesses, Lecture Notes in Physics 36, Springer-Verlag, New York (1975)
6. [Ka] S. Kawashima, Global existence and stability of solutions for discrete velocity models of the Boltzmann equation, Math. Studies 98, Lecture Notes Numer. Appl. Anal. 6, Eds. M. Mimura and T. Nishida, Kinokuniya/North-Holland, 59-85 (1983)
7. [MPB] R. Monaco, M. Pandolfi-Bianchi, T. Platkowski, Shock-waves formation by the discrete Boltzmann equation for binary gas mixtures, Acta-Mech. 84 (1-4), 175-184 (1990)
8. [N] B. Nicolaenko, A general class of nonlinear bifurcation problems from a point in the essential spectrum, and applications to shock wave solutions of kinetic equations, in: Applications of Bifurcation Theory, 333-357, Academic Press, New York (1977)