Advisor Information
Dr. Mahboub Baccouch
Location
Room 112
Presentation Type
Oral Presentation
Start Date
1-3-2019 12:45 PM
End Date
1-3-2019 2:00 PM
Abstract
Description: The Fourier series expansion method is an invaluable approach to solving partial differential equations, including the heat and wave equations. For homogeneous heat and wave equations, the solution can readily be found through separation of variables and then expansion of the solution in terms of the eigenfunctions. Solutions to inhomogeneous heat and wave equations through Fourier series expansion methods were not readily available in the literature for two- and three-dimensional cases. In my previous paper, I developed an approach for solving inhomogeneous heat and wave equations on cubic domains using Fourier series expansion methods. I shall extend my general method of solution for the inhomogeneous heat and wave equations in two and three dimensions with associated boundary and initial conditions from rectangular domains to those with spherical symmetry. For the two-dimensional equations, the domains to be considered shall be a circle and annuli. For the three-dimensional equations, the domain to be considered shall be a sphere
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Included in
Analysis Commons, Harmonic Analysis and Representation Commons, Other Mathematics Commons
Fourier series expansion methods for the heat and wave equations in two and three dimensions on spherical domains
Room 112
Description: The Fourier series expansion method is an invaluable approach to solving partial differential equations, including the heat and wave equations. For homogeneous heat and wave equations, the solution can readily be found through separation of variables and then expansion of the solution in terms of the eigenfunctions. Solutions to inhomogeneous heat and wave equations through Fourier series expansion methods were not readily available in the literature for two- and three-dimensional cases. In my previous paper, I developed an approach for solving inhomogeneous heat and wave equations on cubic domains using Fourier series expansion methods. I shall extend my general method of solution for the inhomogeneous heat and wave equations in two and three dimensions with associated boundary and initial conditions from rectangular domains to those with spherical symmetry. For the two-dimensional equations, the domains to be considered shall be a circle and annuli. For the three-dimensional equations, the domain to be considered shall be a sphere