Analysis of a 1D approximation of the Boltzmann equation: The subclass of grossly determined solutions and the asymptotic behavior of the class of general solutions.

摘要

In this paper we examine an approximation of the Maxwell-Boltzmann equation for a 1D gas. In the manner of classical gas dynamics, we derive a balance law and use it to determine the grossly determined solutions, a sub-class of solutions that are functions dependent on the gas's density field. Then, via spectral decomposition, we derive the class of general solutions and show that they tend asymptotically to the class of grossly determined solutions.