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dc.contributor.advisorChicone, Carmen Charleseng
dc.contributor.authorHeitzman, Michael Thomaseng
dc.date.issued2009eng
dc.date.submitted2009 Falleng
dc.descriptionTitle from PDF of title page (University of Missouri--Columbia, viewed on Feb 26, 2010).eng
dc.descriptionThe 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.descriptionDissertation advisor: Professor Carmen Chicone.eng
dc.descriptionVita.eng
dc.descriptionPh.D. University of Missouri--Columbia 2009 .eng
dc.description.abstractMotivated 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.bibrefIncludes bibliographical references.eng
dc.format.extentv, 102 pageseng
dc.identifier.oclc607354672eng
dc.identifier.urihttps://hdl.handle.net/10355/7017
dc.identifier.urihttps://doi.org/10.32469/10355/7017eng
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcommunityUniversity of Missouri--Columbia. Graduate School. Theses and Dissertationseng
dc.rightsOpenAccess.eng
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
dc.subject.lcshTwo-body problemeng
dc.subject.lcshField theory (Physics)eng
dc.subject.lcshGas dynamics -- Mathematical modelseng
dc.subject.lcshDifferential equationseng
dc.titleA free boundary gas dynamic model as a two-body field theory problemeng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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