dc.contributor.advisor | Chicone, Carmen Charles | eng |
dc.contributor.author | Heitzman, Michael Thomas | eng |
dc.date.issued | 2009 | eng |
dc.date.submitted | 2009 Fall | eng |
dc.description | Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 26, 2010). | eng |
dc.description | The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. | eng |
dc.description | Dissertation advisor: Professor Carmen Chicone. | eng |
dc.description | Vita. | eng |
dc.description | Ph.D. University of Missouri--Columbia 2009 . | eng |
dc.description.abstract | Motivated by the two-body problem in the classical field theories of electrodynamics and gravitation, in which finite propagation speeds lead to radiation reaction and runaway solutions, we develop a free boundary problem in gas dynamics to explore the motion of sources in a medium whose dynamics are governed by hyperbolic, wave-like equations arising from physical conservation laws. In our linearized acoustic model, the fields can be eliminated to yield functional differential equations for the motion of the sources--delay equations with an infinite dimensional state space. Expansion and truncation gives rise to runaway solutions, just as in the classical field theories. We illustrate a scheme for eliminating runaway solutions by reducing to a finite dimensional, globally attracting, invariant manifold on which effective equations of motion for the sources can be obtained. The effective equations of motion approximate the asymptotic behavior of solutions in the full space as they approach the manifold. We also treat the full nonlinear free boundary problem and show that unique classical solutions exist locally, for initial fields close enough to their constant steady state. | eng |
dc.description.bibref | Includes bibliographical references. | eng |
dc.format.extent | v, 102 pages | eng |
dc.identifier.oclc | 607354672 | eng |
dc.identifier.uri | https://hdl.handle.net/10355/7017 | |
dc.identifier.uri | https://doi.org/10.32469/10355/7017 | eng |
dc.language | English | eng |
dc.publisher | University of Missouri--Columbia | eng |
dc.relation.ispartofcommunity | University of Missouri--Columbia. Graduate School. Theses and Dissertations | eng |
dc.rights | OpenAccess. | eng |
dc.rights.license | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. | |
dc.subject.lcsh | Two-body problem | eng |
dc.subject.lcsh | Field theory (Physics) | eng |
dc.subject.lcsh | Gas dynamics -- Mathematical models | eng |
dc.subject.lcsh | Differential equations | eng |
dc.title | A free boundary gas dynamic model as a two-body field theory problem | eng |
dc.type | Thesis | eng |
thesis.degree.discipline | Mathematics (MU) | eng |
thesis.degree.grantor | University of Missouri--Columbia | eng |
thesis.degree.level | Doctoral | eng |
thesis.degree.name | Ph. D. | eng |