Anomalous diffusion limit for the Knudsen gas
Anomalous diffusion limit for the Knudsen gas
复制标题
克努森气体的反常扩散极限
作者：
F. Golse
考虑一种被限制在两个完全相同的平行平板之间的类似分子的稀薄气体;我们将考虑平板之间的距离与平板的尺寸相比非常小的情况。如果气体足够稀薄，就可以忽略容器中分子间碰撞的影响。更确切地说，如果气体分子的平均自由程比容器的所有尺寸都大，则在上述情况下忽略分子间碰撞是合理的。唯一要考虑的碰撞过程是分子对板的碰撞。这种情况的相关数学模型是
Consider a rarefied gas of like molecules confined between two identical parallel plates; we shall be concerned with the case where the distance between the plates is very small when compared to the size of the plates. If the gas is rarefied enough, one can neglect the effect of intermolecular collisions in the container. More precisely, it is legitimate to neglect intermolecular collisions in the situation described above if the mean free path of the gas molecules is large compared to all the dimensions of the container. The only collisional process to be considered is the impingement of the molecules on the plates. The relevant mathematical model for such a situation is