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oai:www.ideals.illinois.edu:2142/45411 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Muncaster, Robert G. DeVille, Robert E. Muncaster, Robert G. Bronski, Jared C. Namachchivaya, N. Sri Carty, Thomas 2013-08-22T16:39:23Z 2013-08-22T16:39:23Z 2013-08 2013-08-22T16:39:23Z 2013-08 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-06-27T18:13:08Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Carty_Thomas.pdf: 548240 bytes, checksum: c85fc7af11e5326bed5f5a3e98d085d4 (MD5) Made available in DSpace on 2013-08-22T16:39:23Z (GMT). No. of bitstreams: 2 Thomas_Carty.pdf: 436307 bytes, checksum: a51bff8059189c02b38717c8ce32631b (MD5) license.txt: 4059 bytes, checksum: dc7c4da67b7c25e428cfa3527e0b1b40 (MD5) http://hdl.handle.net/2142/45411 en Copyright 2013 Thomas Carty Boltzmann Equation Grossly Determined Solutions Spectral Decomposition 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 text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD