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

Carty, Thomas

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https://hdl.handle.net/2142/45411 Copy

Description

Title

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

Author(s)

Carty, Thomas

Issue Date

2013-08-22T16:39:23Z

Director of Research (if dissertation) or Advisor (if thesis)

Muncaster, Robert G.

Doctoral Committee Chair(s)

DeVille, Robert E.

Committee Member(s)

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

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Boltzmann Equation
• Grossly Determined Solutions
• Spectral Decomposition

Abstract

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.

Graduation Semester

2013-08

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

Copyright and License Information

Copyright 2013 Thomas Carty

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