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

Boltzmann Equation;Grossly Determined Solutions;Spectral Decomposition

Carty, Thomas

关键词: Boltzmann Equation;    Grossly Determined Solutions;    Spectral Decomposition;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/45411/Thomas_Carty.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 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 grosslydetermined solutions, a sub-class of solutions that are functions dependent on the gas's densityfield. Then, via spectral decomposition, we derive the class of general solutions and show that they tend asymptotically to the class of grossly determined solutions.