{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/45411"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/45411","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"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","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Carty, Thomas"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Muncaster, Robert G.","DeVille, Robert E.","Bronski, Jared C.","Namachchivaya, N. Sri"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-08-22T16:39:23Z","date_published":"2013-08-22T16:39:23Z","updated_at":"2026-07-22T22:25:34Z","subjects":["Boltzmann Equation","Grossly Determined Solutions","Spectral Decomposition"],"languages":["en"],"rights":["Copyright 2013 Thomas Carty"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/45411","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Muncaster, Robert G.","DeVille, Robert E.","Bronski, Jared C.","Namachchivaya, N. Sri"]},{"key":"dc:creator","label":"Author","values":["Carty, Thomas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-08-22T16:39:23Z","2013-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Boltzmann Equation","Grossly Determined Solutions","Spectral Decomposition"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2013 Thomas Carty"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/45411"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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)"]},{"key":"dc:title","label":"Title","values":["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"]}]}],"canonical_facts":{"dc:contributor":["Muncaster, Robert G.","DeVille, Robert E.","Bronski, Jared C.","Namachchivaya, N. Sri"],"dc:creator":["Carty, Thomas"],"dc:date":["2013-08-22T16:39:23Z","2013-08"],"dc:description":["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)"],"dc:identifier":["http://hdl.handle.net/2142/45411"],"dc:language":["en"],"dc:rights":["Copyright 2013 Thomas Carty"],"dc:subject":["Boltzmann Equation","Grossly Determined Solutions","Spectral Decomposition"],"dc: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"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:34Z"}