Asymptotic methods in kinetic theory of gases: An introduction (Part 1)

Part 1 : The first half of this part is devoted to a brief introduction to kinetic theory of gases, which contains a summary of the Boltzmann equation and its basic properties, the boundary conditions, etc. Then, we consider the free-molecular gas (or the Knudsen gas), i.e., a gas which is so rarefied that the collisions between gas molecules can be neglected (that is, the mean free path of the gas molecules is infinitely long compared with the characteristic length of the system). We present an exact solution that describes the effect of boundary temperature in a quite general situation.