dc.contributor.advisor Pashaev, Oktay K. en dc.contributor.author Ateş, Barış en dc.date.accessioned 2014-07-22T13:52:56Z dc.date.available 2014-07-22T13:52:56Z dc.date.issued 2008 en dc.identifier.uri http://hdl.handle.net/11147/4003 dc.description Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2008 . en dc.description Includes bibliographical references (leaves: 73-74) en dc.description Text in English; Abstract: Turkish and English en dc.description ix, 78 leaves en dc.description.abstract The 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.iso eng en dc.publisher Izmir Institute of Technology en dc.rights info:eu-repo/semantics/openAccess en_US dc.subject.lcc QA372. A864 2008 en dc.subject.lcsh Differential equations, Nonlinear en dc.subject.lcsh Solitions en dc.subject.lcsh Wave equation en dc.subject.lcsh Sturm-Liouville equation en dc.title Nonlinear euler poisson Darboux equations exactly solvable in multidimensions en dc.type masterThesis en dc.contributor.authorID TR110077 dc.contributor.department Izmir Institute of Technology. Mathematics en dc.relation.publicationcategory Tez en_US
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