On the Solution of n-Dimensional Regular Cauchy Problem of Euler-Poisson-Darboux Equation (EPD)
Abstract/ Overview
A general exact solution to the n-dimensional regular Cauchy prob-
lem of Euler-Poisson-Darboux (EPD) equation has been studied. Firstly,
the general exact solution for the one dimensional regular Cauchy prob-
lem of EPD has been worked out. The EPD which is a second order
Partial Di erential Equation (PDE) is converted into an Ordinary Dif-
ferential Equation (ODE) by method of separation of variables. On
solving the ODE, the rst complementary function (cf) is obtained di-
rectly. The second cf is obtained when the rst derivative is eliminated
from the ODE and then the ODE solved. When the expression for
eliminating the rst derivative is solved, a third term is obtained. The
general solution for the one dimensional regular Cauchy EPD is there-
fore the product of the three terms. The procedure has been repeated
for the two dimensional and n-dimensional cases. The general solutions
for these cases are products of four terms and n+2 terms respectively.
Finally, the general exact solution for n-dimensional regular Cauchy
wave equation when k = 0, has also been obtained.
Mathematics Subject Classi cation: 35Q05