| 姜正禄.无限真空中有外力的Enskog方程整体解[J].数学年刊A辑,2009,30(1):43~54 |
| 无限真空中有外力的Enskog方程整体解 |
| Global Solution to Enskog Equation with External Force in Infinite Vacuum |
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| DOI： |
| 中文关键词: Enskog方程 整体解 碰撞算子 |
| 英文关键词:The Enskog equation, Global existence, Collistion operator |
| 基金项目:国家自然科学基金，中俄合作基金，教育部留学回国人员科研启动基金 |
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| 中文摘要: |
| 首先给出对应于带有外力的Enskog方程的次特征方程组的假设.由于Enskog方程的碰撞算子比Boltzmann方程的复杂,所以这些假设比Duan等人就Boltzmann方程给出的复杂.这些假设与中等或更稠密的气体的粒子碰撞有着密切的关系,而且用它们来估计Enskog积分方程中所谓的获得和损失积分.接着,通过控制这些积分,证明用于描述无限真空中中等或更稠密的气体的Enskog方程整体温和解存在唯一.最后,对Enskog方程中碰撞因子的局部Lipschitz假设作些注释. |
| 英文摘要: |
| The author first gives hypotheses of the bicharacteristic equations corresponding
to the Enskog equation with an external force. Since the collision operator of the Enskog
equation is more complicated than that of the Boltzmann equation, these hypotheses are
more complicated than those given by Duan et al. for the Boltzmann equation. The hypotheses
are very related to collision of particles of moderately or highly dense gases along
the bicharacteristic curves and they can be used to make the estimation of the so-called gain
and loss integrals of the Enskog integral equation. Then, by controlling these integrals, it is
shown that there exists a unique global mild solution to the Enskog equation in an infinite
vacuum for moderately or highly dense gases. Finally, the author makes some remarks on
the locally Lipschitz assumption of the collision factors in the Enskog equation. |
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