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On the speed of approach to equilibrium for a collisionless gas
1. | Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 606-8501 |
2. | Ecole Polytechnique, Centre de Mathématiques Laurent Schwartz, 91128 Palaiseau Cedex, France |
References:
[1] |
L. Arkeryd and A. Nouri, Boltzmann asymptotics with diffuse reflection boundary conditions, Monatsh. Math., 123 (1997), 285-298.
doi: 10.1007/BF01326764. |
[2] |
A. V. Bobylev, The theory of the nonlinear, spatially uniform Boltzmann equation for Maxwell molecules, Sov. Sci. Rev. C. Math. Phys., 7 (1988), 111-233 |
[3] |
A. V. Bobylev and C. Cercignani, On the rate of entropy production for the Boltzmann equation, J. Stat. Phys., 94 (1999), 603-618.
doi: 10.1023/A:1004537522686. |
[4] |
C. Cercignani, H-Theorem and trend to equilibrium in the kinetic theory of gases, Arch. Mech., 34 (1982), 231-241. |
[5] |
L. Desvillettes, Entropy dissipation rate and convergence in kinetic equations, Commun. in Math. Phys., 123 (1989), 687-702.
doi: 10.1007/BF01218592. |
[6] |
L. Desvillettes and F. Salvarani, Asymptotic behavior of degenerate linear transport equations, Bull. Math. Sci., 133 (2009), 848-858.
doi: 10.1016/j.bulsci.2008.09.001. |
[7] |
L. Desvillettes and C. Villani, On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation, Invent. Math., 159 (2005), 245-316.
doi: 10.1007/s00222-004-0389-9. |
[8] |
W. Feller, On the integral equation of renewal theory, Ann. Math. Stat., 12 (1941), 243-267.
doi: 10.1214/aoms/1177731708. |
[9] |
Y. Guo, Decay and continuity of the Boltzmann equation in bounded domains, Arch. for Ration. Mech. Anal., 197 (2010), 713-809.
doi: 10.1007/s00205-009-0285-y. |
[10] |
T. Tsuji, K. Aoki and F. Golse, Relaxation of a free-molecular gas to equilibrium caused by interaction with vessel wall, J. Stat. Phys., 140 (2010), 518-543.
doi: 10.1007/s10955-010-9997-5. |
[11] |
S. Ukai, N. Point and H. Ghidouche, Sur la solution globale du problème mixte de l'équation de Boltzmann non linéaire, (French)[On the global solution of the mixed problem for the nonlinear Boltzmann equation], J. Math. Pures Appl. (9), 57 (1978), 203-229. |
[12] |
C. Villani, Cercignani's conjecture is sometimes true and almost always true, Commun. Math. Phys., 234 (2003), 455-490.
doi: 10.1007/s00220-002-0777-1. |
[13] |
C. Villani, "Hypocoercivity,'' Memoirs of the Amer. Math. Soc., 202 (2009), no. 950. |
[14] |
B. Wennberg, Entropy dissipation and moment production for the Boltzmann equation, J. Stat. Phys., 86 (1997), 1053-1066.
doi: 10.1007/BF02183613. |
[15] |
S.-H. Yu, Stochastic formulation for the initial boundary value problems of the Boltzmann equation, Arch. for Ration. Mech. Anal., 192 (2009), 217-274.
doi: 10.1007/s00205-008-0139-z. |
show all references
References:
[1] |
L. Arkeryd and A. Nouri, Boltzmann asymptotics with diffuse reflection boundary conditions, Monatsh. Math., 123 (1997), 285-298.
doi: 10.1007/BF01326764. |
[2] |
A. V. Bobylev, The theory of the nonlinear, spatially uniform Boltzmann equation for Maxwell molecules, Sov. Sci. Rev. C. Math. Phys., 7 (1988), 111-233 |
[3] |
A. V. Bobylev and C. Cercignani, On the rate of entropy production for the Boltzmann equation, J. Stat. Phys., 94 (1999), 603-618.
doi: 10.1023/A:1004537522686. |
[4] |
C. Cercignani, H-Theorem and trend to equilibrium in the kinetic theory of gases, Arch. Mech., 34 (1982), 231-241. |
[5] |
L. Desvillettes, Entropy dissipation rate and convergence in kinetic equations, Commun. in Math. Phys., 123 (1989), 687-702.
doi: 10.1007/BF01218592. |
[6] |
L. Desvillettes and F. Salvarani, Asymptotic behavior of degenerate linear transport equations, Bull. Math. Sci., 133 (2009), 848-858.
doi: 10.1016/j.bulsci.2008.09.001. |
[7] |
L. Desvillettes and C. Villani, On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation, Invent. Math., 159 (2005), 245-316.
doi: 10.1007/s00222-004-0389-9. |
[8] |
W. Feller, On the integral equation of renewal theory, Ann. Math. Stat., 12 (1941), 243-267.
doi: 10.1214/aoms/1177731708. |
[9] |
Y. Guo, Decay and continuity of the Boltzmann equation in bounded domains, Arch. for Ration. Mech. Anal., 197 (2010), 713-809.
doi: 10.1007/s00205-009-0285-y. |
[10] |
T. Tsuji, K. Aoki and F. Golse, Relaxation of a free-molecular gas to equilibrium caused by interaction with vessel wall, J. Stat. Phys., 140 (2010), 518-543.
doi: 10.1007/s10955-010-9997-5. |
[11] |
S. Ukai, N. Point and H. Ghidouche, Sur la solution globale du problème mixte de l'équation de Boltzmann non linéaire, (French)[On the global solution of the mixed problem for the nonlinear Boltzmann equation], J. Math. Pures Appl. (9), 57 (1978), 203-229. |
[12] |
C. Villani, Cercignani's conjecture is sometimes true and almost always true, Commun. Math. Phys., 234 (2003), 455-490.
doi: 10.1007/s00220-002-0777-1. |
[13] |
C. Villani, "Hypocoercivity,'' Memoirs of the Amer. Math. Soc., 202 (2009), no. 950. |
[14] |
B. Wennberg, Entropy dissipation and moment production for the Boltzmann equation, J. Stat. Phys., 86 (1997), 1053-1066.
doi: 10.1007/BF02183613. |
[15] |
S.-H. Yu, Stochastic formulation for the initial boundary value problems of the Boltzmann equation, Arch. for Ration. Mech. Anal., 192 (2009), 217-274.
doi: 10.1007/s00205-008-0139-z. |
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