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dc.contributor.authorPierson, Mark A.en_US
dc.date.accessioned2014-03-14T20:11:11Z
dc.date.available2014-03-14T20:11:11Z
dc.date.issued2005-04-25en_US
dc.identifier.otheretd-04282005-163231en_US
dc.identifier.urihttp://hdl.handle.net/10919/27416
dc.description.abstractWe first provide a detailed background of a geometric projection methodology developed by Professor Roswitha Marz at Humboldt University in Berlin for showing uniqueness and existence of solutions for ordinary differential-algebraic equations (DAEs). Because of the geometric and operator-theoretic aspects of this particular method, it can be extended to the case of infinite-dimensional abstract DAEs. For example, partial differential equations (PDEs) are often formulated as abstract Cauchy or evolution problems which we label abstract ordinary differential equations or AODE. Using this abstract formulation, existence and uniqueness of the Cauchy problem has been studied. Similarly, we look at an AODE system with operator constraint equations to formulate an abstract differential-algebraic equation or ADAE problem. Existence and uniqueness of solutions is shown under certain conditions on the operators for both index-1 and index-2 abstract DAEs. These existence and uniqueness results are then applied to some index-1 DAEs in the area of thermodynamic modeling of a chemical vapor deposition reactor and to a structural dynamics problem. The application for the structural dynamics problem, in particular, provides a detailed construction of the model and development of the DAE framework. Existence and uniqueness are primarily demonstrated using a semigroup approach. Finally, an exploration of some issues which arise from discretizing the abstract DAE are discussed.en_US
dc.publisherVirginia Techen_US
dc.relation.haspartDissert.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectwell-posednessen_US
dc.subjectsystems of partial differential equationsen_US
dc.subjectexistence and uniquenessen_US
dc.subjecthybrid systemsen_US
dc.subjectpartial differential-algebraic equations (PDAE)en_US
dc.subjectabstract differential-algebraic equations (DAE)en_US
dc.titleTheory and Application of a Class of Abstract Differential-Algebraic Equationsen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeememberBorggaard, Jeffrey T.en_US
dc.contributor.committeememberBurns, John A.en_US
dc.contributor.committeememberRussell, David L.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04282005-163231/en_US
dc.contributor.committeecochairHerdman, Terry L.en_US
dc.contributor.committeecochairCliff, Eugene M.en_US
dc.date.sdate2005-04-28en_US
dc.date.rdate2007-04-29
dc.date.adate2005-04-29en_US


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