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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Carty, Thomas

Contributors dc:contributor

• Muncaster, Robert G.
• DeVille, Robert E.
• Bronski, Jared C.
• Namachchivaya, N. Sri

• Boltzmann Equation
• Grossly Determined Solutions
• Spectral Decomposition

Statement dc:rights

• Copyright 2013 Thomas Carty

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/45411

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/45411