Generalized invariant sets for the Boltzmann equation

Mathematical Models and Methods in Applied Sciences

Volumn 7, Issue 4, 1997, Pages 457-476

  Goudon, T ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

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[No Author keywords available]

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EID: 0031488895     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202597000256     Document Type: Article

References (25)

1. K. Asano and S. Ukai, On the Cauchy problem for the Boltzmann equation with a soft potential, Publ. RIMS 18 (1982) 57-99.
2. N. Bellomo and G. Toscani, On the Cauchy problem for the nonlinear Boltzmann equation. Global existence, uniqueness and asymptotic stability, J. Math. Phys. 26 (1985) 334-338.
3. R. Caflish, The Boltzmann equation with a soft potential, Comm. Math. Phys. 74 (1980) 71-95.
4. C. Cercignani, The Boltzmann Equation and its Applications (Springer-Verlag, 1988).
5. C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases (Springer-Verlag, 1994).
6. R. Di Perna and P. L. Lions, On the Cauchy problem for Boltzmann equation: global existence and weak stability, Ann. Math. 130 (1989) 321-366.
7. R. Di Perna and P. L. Lions, Global solutions of Boltzmann's equation and entropy inequality, Arch. Rational Mech. Anal. 114 (1991) 47-55.
8. p regularity of velocity averages, Ann. IHP. An. Non Linéaire 8 (1991) 271-287.
9. F. Golse, P. L. Lions, B. Perthame and R. Sentis, Regularity of the moments of the solution of a transport equation, J. Funct. Anal. 76 (1988) 110-125.
10. H. Grad, Asymptotic theory of the Boltzmann equation, in Rarefied Gas Dynamic, Third Symposium, Paris 1962, ed. J. A. Laurmann (Academic Press, 1963), Vol. 1 pp. 26-59.
11. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, 1980).
12. K. Hamdache, Sur l'existence globale et le comportement asymptotique de quelques solutions de l'équation de Boltzmann, Thèse Doctorat d'Etat, Paris VI (1986).
13. K. Hamdache, Existence in the large and asymptotic behavior for the Boltzmann equation, Japan J. Appl. Math. 2 (1985) 1-15.
14. R. Illner and M. Shinbrot, The Boltzmann equation: global existence for a rare gas in an infinite vacuum, Comm. Math. Phys. 95 (1984) 217-226.
15. S. Kaniel and M. Shinbrot, The Boltzmann equation I: uniqueness and local existence, Comm. Math. Phys. 58 (1978) 65-84.
16. A. Krasnoselskii, Positive Solutions of Operator Equations (P. NoordhofT Ltd., 1954).
17. J. Lindenstrauss and L. Tzafriri, Classical Danach Spaces II, Function Spaces (Springer, 1979).
18. P. L. Lions, Compactness in Boltzmann equation via Fourier integral operators and applications. Parts I, II and III, J. Math. Kyoto Univ. 34 (1994) 391-461; J. Math. Kyoto Univ. 34 (1994) 539-584.
19. P. L. Lions, Compactness in Boltzmann equation via Fourier integral operators and applications. Parts I, II and III, J. Math. Kyoto Univ. 34 (1994) 391-461; J. Math. Kyoto Univ. 34 (1994) 539-584.
20. P. L. Lions, Global solutions of kinetic models and relatedl questions, in Non-equilibrium Problems in Many-Particle Systems, Montecatini 1992, eds. C. Cercignani and M. Pulvirenti, Lect. Notes in Math. Vol. 1551 (Springer, 1993), pp. 58-86.
21. S. Mischler and B. Perthame, Boltzmann equation with infinite energy: renormalized solutions, distributional solutions for small initial data and initial data close to a Maxwellian, preprint (1995).
22. M. Reed and B. Simon, Methods of Modern Mathematical Physics (Academic Press, 1970), Vol. 2.
23. L. Tartar, Topics in nonlinear analysis, Publications de l'Université d'Orsay (1978).
24. L. Tartar, Oscillations and asymptotic behaviour for two semi-linear hyperbolic systems, in Dynamics of Infinite Dimensional Systems, NATO ASI Series, Vol. F37, eds. F. N. Chow and F. K. Hale (Springer-Verlag, 1987), pp. 341-356.
25. G. Toscani, Global solution of the initial value problem for the Boltzmann equation near a local Maxwellian, Arch. Rational Mech. Anal. 102 (1988) 231-241.