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dc.contributor.authorAoki, Yasunori
dc.date.accessioned2012-08-29 16:24:30 (GMT)
dc.date.available2012-08-29 16:24:30 (GMT)
dc.date.issued2012-08-29T16:24:30Z
dc.date.submitted2012
dc.identifier.urihttp://hdl.handle.net/10012/6908
dc.description.abstractIn this thesis, we explore two important aspects of study of differential equations: analytical and computational aspects. We first consider a partial differential equation model for a static liquid surface (capillary surface). We prove through mathematical analyses that the solution of this mathematical model (the Laplace-Young equation) in a cusp domain can be bounded or unbounded depending on the boundary conditions. By utilizing the knowledge we have obtained about the singular behaviour of the solution through mathematical analysis, we then construct a numerical methodology to accurately approximate unbounded solutions of the Laplace-Young equation. Using this accurate numerical methodology, we explore some remaining open problems on singular solutions of the Laplace-Young equation. Lastly, we consider ordinary differential equation models used in the pharmaceutical industry and develop a numerical method for estimating model parameters from incomplete experimental data. With our numerical method, the parameter estimation can be done significantly faster and more robustly than with conventional methods.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectPartial Differential Equationsen
dc.subjectPharmacokineticsen
dc.subjectLaplace-Young Equationen
dc.subjectNumerical Approximationen
dc.titleStudy of Singular Capillary Surfaces and Development of the Cluster Newton Methoden
dc.typeDoctoral Thesisen
dc.comment.hiddenMy thesis contains two published works. One was published by Elsevier and the following is their copyright statement states: What rights do I retain as a journal author? the right to include the journal article, in full or in part, in a thesis or dissertation; http://www.elsevier.com/wps/find/journaldescription.cws_home/505613/authorinstructions#N10B28 Another was published by Pacific Journal of Mathematics and their copyright agreement states: The Author(s) may use part or all of this Work or its image in any future works of his/her (their) own. http://msp.berkeley.edu/editorial/uploads/pjm/accepted/110617-Aoki/copyright.pdf I wish to graduate at Oct 2012 convocation so I sincerely appreciate if you could review my thesis on time for the deadline.en
dc.pendingfalseen
dc.subject.programApplied Mathematicsen
uws-etd.degree.departmentApplied Mathematicsen
uws-etd.degreeDoctor of Philosophyen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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