On an initial boundary value problem involving the generalized EPD equation

Abstract

In the present paper, a solution is given to the following singular initial boundary value problem u(0,t)=u(a,t) = 0, u(x,0) = l, $frac{u}{t}(x,0)=0,frac{partial^p u}{partial t^p}(x,0)=frac{1}{p!}(p=2,3,...,m-1)$, for the homogeneous generalized Euler Poisson Darboux equation $Delta u-frac{partial^m u}{partial t^m}-sumlimits_{p=1}^{m-1}frac{k_p}{t^p}frac{partial^{m-p} u}{partial t^{m-p}}-k_m u=0$,where x, a $inBbb{R}^n, k_1,k_2,...,k_m $ are real parameters, t is the time variable and $Delta$ is the n-dimensional Laplace operator, The solution is obtained using the finite integral transformation method and is given in terms of absolutely and uniformly convergent power series.