Optimization Problem for Klein-Gordon Equation

dc.contributor.advisorGutman, Semion
dc.creatorLuo, Qinghua
dc.date.accessioned2019-04-27T21:41:47Z
dc.date.available2019-04-27T21:41:47Z
dc.date.issued2012
dc.description.abstractWe consider a damped Klein-Gordon equation with a variable diffusion coefficient. The goal is to derive necessary conditions for the optimal set of parameters minimizing the objective function J. First, we show that the solution map is continuous. Then the solution map is shown to be weakly Gateaux differentiable on the admissible set P, implying the Gateaux differentiability of the objective function. Finally we study the Frechet differentiability of J and optimal parameters for these problems. Unlike the sine-Gordon equation, which has a bounded nonlinear term, Klein-Gordon equation requires stronger assumptions on the initial data.
dc.format.extent76 pages
dc.format.mediumapplication.pdf
dc.identifier9999643002042
dc.identifier.urihttps://hdl.handle.net/11244/319366
dc.languageen_US
dc.relation.requiresAdobe Acrobat Reader
dc.subjectKlein-Gordon equation
dc.thesis.degreePh.D.
dc.titleOptimization Problem for Klein-Gordon Equation
dc.typetext
dc.typedocument
ou.groupCollege of Arts and Sciences::Department of Mathematics

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