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Long Time Behavior of the Fokker-Planck-Boltzmann Equation

Long Time Behavior of the Fokker-Planck-Boltzmann Equation
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摘要 This paper is devoted to the existence and long time behavior of the global classical solution to Fokker-Planck-Boltzmann equation with initial data near the absolute Maxwellian. This paper is devoted to the existence and long time behavior of the global classical solution to Fokker-Planck-Boltzmann equation with initial data near the absolute Maxwellian.
作者 Ming-ying ZHONG Hai-liang LI
机构地区 Department of Mathematical and Information Sciences Department of Mathematics
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2014年第2期533-554,共22页 应用数学学报（英文版）
基金 supported by the National Natural Science Foundation of China(No.11301094) supported by the National Natural Science Foundation of China(No.11171228,11231006 and 11225102) the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions(No.CIT&TCD20140323)
关键词 Fokker-Planck-Boltzmann equation global existence long time behavior Fokker-Planck-Boltzmann equation, global existence, long time behavior
分类号 O175 [理学—基础数学]
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参考文献22

  • 1Bellomo, N. Toscani, G. On the Cauchy problem for the nonlinear Boltzmann equation: global existence, uniqueness and asymptotic behaviour. J. Math. Phys. 26:334-338 (1985).
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  • 3DiPerna, R.J. Lion, P.L. On the Cauchy problem for Boltzmann equation: global existence and weak stability. Ann. Math. 130:321-366 (1989).
  • 4DiPerna, R.J. Lion, P.L. On the Fokker-Planck-Boltzmann equation. Comm. Math. Phys. 120:1-23 (1988).
  • 5Duan, R.J. Yang, T. Zhu, C.J. Boltzmann equation with external force and Vlasov-Poisson-loltzmann system in infinite vacuum. Discrete and Continuous Dynamical Systems, 16:253-277 (2006).
  • 6Duan, R.J. Ukai, S. Yang, T. Zhao, H.J. Optimal decay estimates on the linearized Boltzmann equation with time dependent force and their applications. Comm. Math. Phys. 277:189-236 (2008).
  • 7Glassey, R.T. The Cauchy Problem in Kinetic Theory. SIAM, Philadephia, PA, 1996.
  • 8Golse, F. Perthame, B. Sulem, C. On a boundary layer problem for the nonlinear Boltzmann equation. Arch. Ration. Mech. AnaL, 103:81-96 (1988).
  • 9Grad, H. Asymptotic theory of Boltzmann equation Ⅱ. Rarefied Gas Dynamics. Ed. J.A. Laurmann, Vol.I, 26-59, Academic Press, New York, 1963.
  • 10Guo, Y. The Boltzmann equation in the whole sapce. Indiana Univ. Math. J. 53:1081-1094 (2004).
Acta Mathematicae Applicatae Sinica
2014年 第2期

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