Nonlinear euler poisson darboux equations exactly solvable in multidimensions
by
Ateş, Barış.
Title
:
Nonlinear euler poisson darboux equations exactly solvable in multidimensions
Author
:
Ateş, Barış.
Personal Author
:
Ateş, Barış.
Publication Information
:
[s.l.]: [s.n.], 2008.
Physical Description
:
ix, 78 leaves.: ill. + 1 computer laser optical disc.
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.
Subject Term
:
Differential equations,Nonlinear.
Solitions.
Wave equation.
Sturm-Liouville equation
Added Author
:
Pashaev, Oktay K.
Added Corporate Author
:
İzmir Institute of Technology. Mathematics.
Added Uniform Title
:
Thesis (Master)--İzmir Institute of Technology: Mathematics.
İzmir Institute of Technology: Mathematics--Thesis (Master).
Electronic Access
:
Library | Material Type | Item Barcode | Shelf Number | Status |
---|
IYTE Library | Thesis | T000682 | QA372 .A864 2008 | Tez Koleksiyonu |
IYTE Library | Supplementary CD-ROM | ROM1065 | QA372 .A864 2008 EK1 | Tez Koleksiyonu |