The Steady State of Dissipative Boltzmann Equation

Xiao Zhi-tao; Jin Shou-bo

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The Steady State of Dissipative Boltzmann Equation

更新时间：2026-05-27

- The Steady State of Dissipative Boltzmann Equation
- Vol. 26, Issue 1, Pages: 12(2009)
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- Online First：01 January 2009，
  
  Published：2009
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肖志涛, 晋守博. 耗散Boltzmann方程的稳定态解[J]. 广东工业大学学报, 2009, 26(1): 12.

Xiao Zhi-tao, Jin Shou-bo. The Steady State of Dissipative Boltzmann Equation[J]. 2009, 26(1): 12.
肖志涛, 晋守博. 耗散Boltzmann方程的稳定态解[J]. 广东工业大学学报, 2009, 26(1): 12. DOI：

Xiao Zhi-tao, Jin Shou-bo. The Steady State of Dissipative Boltzmann Equation[J]. 2009, 26(1): 12. DOI：

摘要

考虑满足质量和动量守恒、能量耗散的空间齐次Boltzmann方程

通过Pseudo-Maxwellian逼近处理

证明了系统稳定态解存在性、唯一性和正则性.

Abstract

It studies the spatially homogeneous dissipative Boltzmann equation.For solutions satisfying conservation of mass and momentum

and decreasing of energy

in the Pseudo-Maxwellian approximation

the uniqueness and regularity of the steady state of the equation are established.

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references

M. Bisi,J. A. Carrillo,G. Toscani. Contractive Metrics for a Boltzmann Equation for Granular Gases: Diffusive Equilibria[J], 2005

Bertrand Lods,Giuseppe Toscani. Dissipative Linear Boltzmann Equation for Hard Spheres[J], 2004

A. V. Bobylev,C. Cercignani. Moment Equations for a Granular Material in a Thermal Bath[J], 2002

A. V. Bobylev,J. A. Carrillo,I. M. Gamba. On Some Properties of Kinetic and Hydrodynamic Equations for Inelastic Interactions[J], 2000

G. Toscani,C. Villani. Probability Metrics and Uniqueness of the Solution to the Boltzmann Equation for a Maxwell Gas[J], 1999

E. A. Carlen,E. Gabetta,G. Toscani. Propagation of Smoothness and the Rate of Exponential Convergence to Equilibrium for a Spatially Homogeneous Maxwellian Gas[J], 1999

G. Gabetta,G. Toscani,B. Wennberg. Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation[J], 1995

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