Analysis of Self-Organization

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dc.contributor.advisorMellet, Antoineen_US
dc.contributor.authorDelgadino, Matias Gonzaloen_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2016-06-22T06:05:41Z
dc.date.available2016-06-22T06:05:41Z
dc.date.issued2016en_US
dc.description.abstractThe dissertation is devoted to the study of problems in calculus of variation, free boundary problems and gradient flows with respect to the Wasserstein metric. More concretely, we consider the problem of characterizing the regularity of minimizers to a certain interaction energy. Minimizers of the interaction energy have a somewhat surprising relationship with solutions to obstacle problems. Here we prove and exploit this relationship to obtain novel regularity results. Another problem we tackle is describing the asymptotic behavior of the Cahn-Hilliard equation with degenerate mobility. By framing the Cahn-Hilliard equation with degenerate mobility as a gradient flow in Wasserstein metric, in one space dimension, we prove its convergence to a degenerate parabolic equation under the framework recently developed by Sandier-Serfaty.en_US
dc.identifierhttps://doi.org/10.13016/M29497
dc.identifier.urihttp://hdl.handle.net/1903/18328
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledCahn-Hilliarden_US
dc.subject.pquncontrolledGradient Flowsen_US
dc.subject.pquncontrolledInteraction Energyen_US
dc.subject.pquncontrolledObstacle Problemen_US
dc.subject.pquncontrolledPotential Theoryen_US
dc.subject.pquncontrolledSelf-Organizationen_US
dc.titleAnalysis of Self-Organizationen_US
dc.typeDissertationen_US

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