On the stationary Povzner equation in Rn

Kyoto Journal of Mathematics

Volumn 39, Issue 1, 1999, Pages 115-153

  Arkeryd, L ^a   Nouri, A ^a  

^a NONE

Author keywords

[No Author keywords available]

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EID: 0033412797     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1250517956     Document Type: Article

References (34)

1. L. Arkeryd, C. Cercignani and R. Illner, Measure solutions of the steady Boltzmann equation in a slab, Comm. Math. Phys., 142 (1991), 285-296.
2. L. Arkeryd and N. Maslova. On diffuse reflection at the boundary for the Boltzmann equation and related equations, J. Stat. Phys., 77 (1994), 1051-1077.
3. L. Arkeryd and A. Nouri. A compactness result related to the stationary Boltzmann equation in a slab, with applications to the existence theory, Ind. Univ. Math. Journ., 44 (1995), 815-839.
4. L. Arkeryd and A. Noun. On the stationary Boltzmann equation for the slab and the half-line, in preparation.
5. L. Arkeryd and A. Nouri. Asymptotics of the Boltzmann equation with diffuse reflection boundary conditions. Mh. Math., 123 (1997), 285-298.
6. A. V. Bobylev and G. Spiga, On a class of exact two-dimensional stationary solutions for the Broadwell model of the Boltzmann equation, J. Phys. A. Math. Gen., 27 (1994), 7451-7459.
7. A. V. Bobylev and G. Toscani. Two-dimensional half space problems for the Broadwell discrete velocity model, to appear in Continuum Mech. Thermodyn.
8. P. Broman, On a class of boundary value problems for the Povzner equation. Preprint Gothenburg 1993.
9. C. Cercignani, The Boltzmann equation and its applications. Springer, Berlin, 1988.
10. C. Cercignani, The Grad limit for a system of soft spheres, Comm. Pure Appl. Math., 36 (1983), 479-494.
11. C. Cercignani, Steady solutions of the nonlinear Boltzmann equation, Transp. Th. Stat. Phys., to appear.
12. C. Cercignani and M. Giurin, Measure solutions of the steady linear Boltzmann equation in a slab, Transp. Th. Stat. Phys., to appear.
13. C. Cercignani, R. Illner and M. Shinbrot, A boundary value problem for the two-dimensional Broadwell model, Com. Math. Phys., 114 (1985), 687-698.
14. C. Cercignani, R. Illner, M. Shinbrot and M. Pulvirenti, On non linear stationary half-space problems in discrete kinetic theory, J. Stat. Phys., 52 (1988), 885-896.
15. H. Cornille, Exact (2+1)-dimensional solutions for two discrete velocity models with two independent densities, J. Phys. A, Math. Gen., 20 (1987), 1063-1067.
16. F. Coron, F. Golse and C. Sulem, Classification of kinetic layer problems, Comm. Pure Appl. Math., 41 (1988), 409-435.
17. F. Golse, P. L. Lions, B. Perthame and R. Sentis, Regularity of the moments of the solution of a transport equation, J. Func. Anal., 76 (1988), 110-125.
18. H. Grad, High frequency sound recording according to the Boltzmann equation, J. SIAM Appl. Math., 14 (1966), 935-955.
19. J. P. Guiraud, Problème aux limites intérieur pour l'équation de Boltzmann en régime stationnaire faiblement non linéaire, J. Mécanique, 11 (1972), 183-231.
20. A. Heintz, Solvability of a boundary problem for the non linear Boltzmann equation in a bounded domain, Aerodynamics of rarefied gases 10 (1980), 16-24, Leningrad Univ., Leningrad.
21. R. Illner and J. Struckmeier, Boundary value problems for the steady Boltzmann equation, J. Stat. Phys., 85 (1996), 427-454.
22. M. Krook, Dynamics of rarefied gases, Phys. Rev., 99 (1955), 1896-1897.
23. M. Lachowicz, Solutions of nonlinear kinetic equations on the level of Navier-Stokes dynamics, J. Math. Kyoto Univ., 32 (1992), 31-43.
24. M. Lachowicz, and M. Pulvirenti, A stochastic system of particles modelling the Euler equations, Arch. Rat. Mech. Anal., 109 (1990), 81-93.
25. P. L. Lions, Compactness in Boltzmann's equation via Fourier integral operator and applications, J. Math. Kyoto Univ., 34 (1994), 391-427.
26. N. Maslova, Existence and uniqueness of stationary solutions of the linearised Boltzmann equation in a bounded domain, Non linear evolution equations, Kinetic approach, Series on advances in Mathematics for Applied Sciences, Vol 10, World Scientific, 1993.
27. N. Maslova, The solvability of internal stationary problems for Boltzmann's equation at large Knudsen numbers, USSR Comp. Math. & Math. Phys., 17 (1977), 194-204.
28. D. Morgenstern, Analytical studies related to the Maxwell-Boltzmann equation, J. Rat. Mech. Anal., 4 (1955), 533-555.
29. Y. P. Pao, Boundary-value problems for the linearized and weakly nonlinear Boltzmann equation, J. Math. Phys., 8 (1967), 1893-1898.
30. A. Y. Povzner, The Boltzmann equation in kinetic theory of gases, Amer. Math. Soc. Transl., Ser. 2 47 (1962), 193-216.
31. R. Pettersson, On convergence to equilibrium for the linear Boltzmann equation without detailed balance assumptions. Rarefied gas dynamics, 19 (1995), 107-113, Oxford UP.
32. L. Triolo, A formal generalization of the H-theorem in kinetic theory, Report, Roma Tor Vergata, 1993.
33. S. Ukai and K. Asano, Steady solutions of the Boltzmann equation for a gas flow past an obstacle; I Existence, Arch. Rat. Mech. Anal., 84 (1983), 249-291.
34. B. Wennberg, Regularity in the Boltzmann equation and the Radon transform, Comm. Part. Diff. Eqs., 19 (1994), 2057-2074.