Fractional diffusion limit for collisional kinetic equations: A moments method
Fractional diffusion limit for collisional kinetic equations: A moments method
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碰撞动力学方程的分数扩散极限：矩法
DOI：
10.1512/iumj.2010.59.4128
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
A. Mellet
中科院分区：
文献类型：
--
作者：
A. Mellet
本文讨论了当平衡点用重尾分布函数而不是麦克斯韦分布描述时，线性动力学方程的水动力极限。我们表明，长时间/小平均自由程行为的动力学方程的解决方案描述的分数扩散方程。我们介绍的方法是有点让人想起所谓的“矩法”，它在动力学理论中起着重要的作用。
This paper is devoted to hydrodynamic limits of linear kinetic equations when the thermodynamical equilibrium is described by a heavy-tail distribution function rather than a Maxwellian distribution. We show that the long time/small mean free path behavior of the solution of the kinetic equation is described by a fractional diffusion equation. The method that we introduce is somewhat reminiscent of the so-called "moments method" which plays an important role in kinetic theory.