Free Cooling and High-Energy Tails of Granular Gases with Variable Restitution Coefficient
Free Cooling and High-Energy Tails of Granular Gases with Variable Restitution Coefficient
复制标题
具有可变恢复系数的颗粒气体的自然冷却和高能尾部
DOI：
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发表时间：
2009
影响因子：
2
通讯作者：
B. Lods
中科院分区：
文献类型：
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作者：
R. Alonso;B. Lods
我们证明了所谓的广义哈夫定律产生的最佳代数冷却速率的颗粒气体的温度所描述的均匀玻尔兹曼方程的非弹性相互作用与非常数恢复系数。我们的分析是通过仔细研究的无限系统的时刻的解决方案的Boltzmann方程的颗粒气体和精确的Lp估计的自相似变量。在这个过程中，我们推广的玻尔兹曼碰撞算子最近获得的均匀颗粒气体与常数恢复系数的更广泛的一类物理恢复系数，取决于碰撞碰撞速度的几个结果。这个推广导致了所谓的L1指数尾定理。用于此模型。
We prove the so-called generalized Haff's law yielding the optimal algebraic cooling rate of the temperature of a granular gas described by the homogeneous Boltzmann equation for inelastic interactions with non constant restitution coefficient. Our analysis is carried through a careful study of the infinite system of moments of the solution to the Boltzmann equation for granular gases and precise Lp estimates in the selfsimilar variables. In the process, we generalize several results on the Boltzmann collision operator obtained recently for homogeneous granular gases with constant restitution coefficient to a broader class of physical restitution coefficients that depend on the collision impact velocity. This generalization leads to the so-called L1-exponential tails theorem. for this model.