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dc.contributor.advisorPashaev, Oktay K.en
dc.contributor.authorAteş, Barışen
dc.date.accessioned2014-07-22T13:52:56Z
dc.date.available2014-07-22T13:52:56Z
dc.date.issued2008en
dc.identifier.urihttp://hdl.handle.net/11147/4003
dc.descriptionThesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2008 .en
dc.descriptionIncludes bibliographical references (leaves: 73-74)en
dc.descriptionText in English; Abstract: Turkish and Englishen
dc.descriptionix, 78 leavesen
dc.description.abstractThe method of spherical means is the well known and elegant method of solving initial value problems for multidimensional PDE. By this method the problem reduced to the 1+1 dimensional one, which can be solved easily. But this method is restricted by only linear PDE and can not be applied to the nonlinear PDE. In the present thesis we study properties of the spherical means and nonlinear PDE for them. First we briefly review the main definitions and applications of the spherical means for the linear heat and the wave equations. Then we study operator representation for the spherical means, especially in two and three dimensional spaces. We find that the spherical means in complex space are determined by modified exponential function. We study properties of these functions and several applications to the heat equation with variable diffusion coefficient.Then nonlinear wave equations in the form of the Liouville equation, the Sine-Gordon equation and the hyperbolic Sinh-Gordon equations in odd space dimensions are introduced. By some combinations of functions we show that models are reducible to the 1+1 dimensional one on the half line.The Backlund transformations and exact particular solutions in the form of progressive waves are constructed. Then the initial value problem for the nonlinear Burgers equation and the Liouville equations are solved. Application of our solutions to spherical symmetric multidimensional problems is discussed.en
dc.language.isoengen
dc.publisherIzmir Institute of Technologyen
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subject.lccQA372. A864 2008en
dc.subject.lcshDifferential equations, Nonlinearen
dc.subject.lcshSolitionsen
dc.subject.lcshWave equationen
dc.subject.lcshSturm-Liouville equationen
dc.titleNonlinear euler poisson Darboux equations exactly solvable in multidimensionsen
dc.typemasterThesisen
dc.contributor.authorIDTR110077
dc.contributor.departmentIzmir Institute of Technology. Mathematicsen
dc.relation.publicationcategoryTezen_US


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