Browsing by Author "Hailu Tafesse"

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    Duhamel’s Principle and the Method of Descent for the Wave Equation
    (Addis Ababa University, 2014-06) Hailu Tafesse; Abdi Tadesse (PhD)
    In this project we present investigation of the linear wave equation with the unknown function u, subject to prescribed initial and/or boundary data, where Δ is n-dimensional Laplacian. In 1d, the solution of IVP is rendered by first reducing it into lower order PDE and then appealing to the method of characteristics, while, for BVP the method of reflection is employed to yield the pertinent solution. In higher dimension, explicit solution of IVP is derived as based on the method of spherical mean and the method of descent. In the sequel, Duhamel’s principle is used to get the solution of non-homogeneous wave equation from the associated homogeneous wave equation