The Tanaka functional and exponential convergence for non cut-off molecules

Transport Theory and Statistical Physics

Volumn 25, Issue 3-5, 1996, Pages 543-554

  Gabetta, E ^a   Toscani, G ^a   Wennberg, B ^b  

^a UNIVERSITY OF PAVIA   (Italy)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030491995     PISSN: 00411450     EISSN: None     Source Type: Journal    
DOI: 10.1080/00411459608220720     Document Type: Article

References (12)

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3. H. Tanaka, An inequality for a functional of probability distributions and its application to Kac's one-dimensional model of a Maxwellian gas, Wahrsch. Verw. Geb. 27, 47-52 (1973).
4. G. Toscani, Bivariate distributions with given marginals and applications to kinetic theory of gases, Atti Convegno Naz. AIMETA di Meccanica Stocastica, Taormina (1993).
5. M. Kac, Probability and related topics in the physical sciences, New York (1959).
6. H.P. McKean Jr., Speed of approach to equilibrium for Kac's caraicature of a Maxwellian gas, Arch. Rational Mech. Anal. 21, 343-367 (1966).
7. L. Desvillettes, About the regularizing properties of the non-cut-off Kac equation, Comm. Math. Phys. 168, 417-440 (1995).
8. E. Gabetta, L. Pareschi, About the non cut-off Kac equation: uniqueness and asymptotic behaviour, preprint 911/94, Istituto di Analisi Numerica del CNR, Pavia (1994).
9. E. Gabetta, G. Toscani, On convergence to equilibrium for Kac's caricature of a Maxwell gas, J. Math. Physics, 35, 190-208 (1994).
10. T. Carleman, Sur la solution de l'equation intégrodifferential de Boltzmann, Acta Math. 60, 91-146 (1933).
11. E. Gabetta, G. Toscani, B. Wennberg, Metrics for probability measures and the trend to equilibrium for solutions of the Boltzmann equation, J. Stat. Phys. 81 no 5/6, 901-934 (1995).
12. 1-asymptotics for the space-homogeneous Boltzmann equation, in Advances in analysis, probability and mathematical physics, S. Albeverio, W.A.J. Luxemburg, M. Wolff eds., Kluwer, Dortrecht (1994).