Some investigations on singular cauchy problems
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Date
2011-11-17
Authors
Iyaya, Wanjala
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Abstract
The purpose of our study is to get a solution to the Cauchy problem of
(i) The wave equation in n-dimension space Rn which is effectively a good example of regular Cauchy problems
(ii) The Euler Poisson Darboux equation which we call singular Cauchy problem by use of Riemann's method.
The Riemann-Green function for each case is calculated, which enables us to evaluate any solution at a point by the Cauchy data on a non-characteristic curve.
In case (i) the Riemann-Green function is in terms of Legendre polynomial and the solution obtained is shown to solve the wave equation as well.
In case (ii) the Riemann-Green function written in terms of the Appell's hyper geometric function of two variables is arrived at, this is of interest and may be a good model for a more general theory.
A discussion of the generalized singular Cauchy problem of Euler-Poisson-Darboux equation is included and found to have solution that is continuous and analytic over the interval that contains the singular point.
Description
Department of Mathematics,69p.The QA 377.W3 2008.
Keywords
Cauchy problem, Differential equations, partial