Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation

Asymptotic Analysis

Volumn 46, Issue 3-4, 2006, Pages 349-359

  Hérau, Frédéric ^a  

^a UNIVERSITÉ DE REIMS CHAMPAGNE ARDENNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOLTZMANN EQUATION; COLLISION OPERATOR; FOKKER-PLANCK EQUATION;

DIFFUSION; LINEAR EQUATIONS; MAXWELL EQUATIONS;

RELAXATION PROCESSES;

EID: 33644593563     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

1. M.-J. Cáceres, J.-A. Carrillo and T. Goudon, Equilibration rate for the linear inhomogeneous relaxation-time Boltzmann equation for charged particles, Comm. Partial Differential Equations 28(5-6) (2003), 969-989.
2. L. Desvillettes and C. Villani, On the trend to global equilibrium in spatially inhomogeneous systems. Part I: The linear Fokker-Planck equation, Comm. Pure Appl. Math. 54(1) (2001), 1-42.
3. L. Desvillettes and C. Villani, On the trend to global equilibrium for spatially inhomogeneous systems: the Boltzmann equation, Invent. Math. 105(1) (2004).
4. B. Helffer and F. Nier, Hypoellipticity and Spectral Theory for Fokker-Planck Operators and Witten Laplacians, Prépublication 03-25 Université de Rennes, Septembre 2003, to appear in Lecture Notes in Math., Vol. 1862, with the title Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians (2005).
5. F. Hérau, Short and long time behavior of the Fokker-Planck equation in a confining potential and applications, preprint.
6. F. Hérau and F. Nier, Isotropic hypoellipticity and trend to equilibrium for the Fokker-Planck equation with high degree potential, Arch. Rational Mech. Anal. 171(2) (2004), 151-218
7. announced in Actes colloque EDP Forges-les-eaux, 12 p., 2002.
8. F. Hérau, J. Sjöstrand and C. Stolk, Semiclassical analysis for the Kramers-Fokker-Planck equation, Comm. Partial Differential Equations (2005), to appear.
9. C. Villani, A review of mathematical topics in collisional kinetic theory, in: Handbook of Fluid Mechanics, Vol. 1, S. Friedlander and D. Serre, eds, 2003.
10. C. Villani, A review of mathematical topics in collisional kinetic theory, in: Handbook of Mathematical Fluid Dynamics, Vol. I, North-Holland, Amsterdam, 2002, pp. 71-305.