论文信息 - Exact Eternal Solutions of the Boltzmann Equation - 字舞流文

Exact Eternal Solutions of the Boltzmann Equation

We construct two families of self-similar solutions of the Boltzmann equation in an explicit form. They turn out to be eternal and positive. They do not possess finite energy. Asymptotic properties of the solutions are also studied.

Carlo Cercignani | C. Cercignani | A. Bobylev | Alexander Bobylev

[1] A. Bobylev. Exact solutions of the Boltzmann equation , 1975 .

[2] M. H. Ernst,et al. Nonlinear model-Boltzmann equations and exact solutions , 1981 .

[3] On a class of solutions of the Krook–Tjon–Wu model of the Boltzmann equation , 1980 .

[4] The velocity distribution function in an infinitely strong shock wave , 2000 .

[5] Carlo Cercignani,et al. The structure of an infinitely strong shock wave , 1999 .

[6] C. Cercignani,et al. Self-Similar Solutions of the Boltzmann Equation and Their Applications , 2002 .

[7] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1951 .

[8] I. S. Gradshteyn,et al. Table of Integrals, Series, and Products , 1976 .

[9] P. A. P. Moran,et al. An introduction to probability theory , 1968 .

[10] Cédric Villani,et al. Contribution à l'étude mathématique des équations de Boltzmann et de Landau en théorie cinétique des gaz et des plasmas , 1998 .

[11] A. Bobylev,et al. Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwellian gas , 1984 .

[12] T. Wu,et al. Formation of Maxwellian Tails , 1976 .