论文标题
线性化玻尔兹曼碰撞算子：I。由离散的内部能量和多组分混合物建模的多原子分子
Linearized Boltzmann Collision Operator: I. Polyatomic Molecules Modeled by a Discrete Internal Energy Variable and Multicomponent Mixtures
论文作者
论文摘要
Boltzmann方程的线性碰撞运算符可以自然方式写为正乘算子，碰撞频率和积分操作员的总和。单变性单物种的积分算子的紧凑性是经典的结果，而最近获得了混合物的相应结果。在这项工作中，研究了通过离散的内部能量变量建模的多原子单物种的操作员的紧凑性。通过证明积分操作员是Hilbert-Schmidt积分运算符和大约Hilbert-Schmidt积分运算符的总和，在碰撞运算点的概率配方作为起点时，可以获得紧凑性。线性化碰撞算子的自相关性随之而来。此外，对于硬球模型，获得了碰撞频率的界限 - 包括 - 碰撞频率。然后是线性化碰撞操作员是弗雷德姆操作员。 结果可以扩展到混合物。简而言之，仅考虑了单一物种混合物的情况。
The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral operator. Compactness of the integral operator for monatomic single species is a classical result, while corresponding result for mixtures is more recently obtained. In this work the compactness of the operator for polyatomic single species, where the polyatomicity is modeled by a discrete internal energy variable, is studied. With a probabilistic formulation of the collision operator as a starting point, compactness is obtained by proving that the integral operator is a sum of Hilbert-Schmidt integral operators and approximately Hilbert-Schmidt integral operators, under some assumptions on the collision kernel. Self-adjointness of the linearized collision operator follows. Moreover, bounds on - including coercivity of - the collision frequency are obtained for a hard sphere model. Then it follows that the linearized collision operator is a Fredholm operator. The results can be extended to mixtures. For brevity, only the case of mixtures for monatomic species is accounted for.
