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dc.contributor.authorYolcu, Türkayen_US
dc.date.accessioned2009-08-26T18:17:03Z
dc.date.available2009-08-26T18:17:03Z
dc.date.issued2009-07-07en_US
dc.identifier.urihttp://hdl.handle.net/1853/29760
dc.description.abstractIn this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite "entropy", we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method is revealed to be a powerful tool for proving convergence of our algorithm. Finally, we analyze uniqueness and stability of our solution in L¹.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectLagrangianen_US
dc.subjectPDEen_US
dc.subjectParabolic equationsen_US
dc.subjectVariational methoden_US
dc.subjectDe Giorgien_US
dc.subjectOptimizationen_US
dc.subject.lcshDifferential equations, Parabolic
dc.subject.lcshLagrangian functions
dc.subject.lcshInterpolation
dc.subject.lcshAlgorithms
dc.titleParabolic systems and an underlying Lagrangianen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Gangbo, Wilfrid; Committee Member: Chow, Shui-Nee; Committee Member: Harrell, Evans; Committee Member: Swiech, Andrzej; Committee Member: Yezzi, Anthony Josephen_US


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