In this paper some insight into the behavior of the one-particle distribution function describing the Knudsen gas in a convex-plane domain is given. The influence of different kinds of boundary conditions is studied, namely of those following ergodic or chaotic reflection laws and of those with a stable periodic orbit. By applying numerical and theoretical methods it is shown that, under appropriate boundary conditions and after a sufficiently long period of time, there appear enclaves free of particles in the configuration space, and moreover the collection of limiting velocities reached by every particle is finite. On the basis of this result we prove that the one-particle distribution function becomes nonanalytic after a sufficiently long period of time, independent of the initial conditions. On the other hand, it turns out that in our model ergodicity or chaotic properties of the reflection law imply ergodicity or chaotic behavior of the Knudsen gas, respectively. From this result some related properties of the one-particle distribution function of the corresponding Knudsen gas for long periods of time are deduced.

• Received 25 April 1991

DOI:https://doi.org/10.1103/PhysRevA.44.3615