Turkish Journal of Mathematics
DOI
-
Abstract
In this paper, a solution is given for the following initial boundary value problem: \Delta=u_{tt}+k/t+u_t+g(x, t) (t>0) u(0, t)=u(a, t)=0 u(x, 0)=f(x), u_t(x, 0)=0 where x, a \epsilon R^n, t is the time variable, k < 1, k ? -1, -2, -3, . . . is a real parameter, \Delta is the n dimensional Laplace operator, f and g real analytic functions. The equation in this problem is known as the nonhomogeneous Euler-Poisson-Darboux (E.P.D.) Equation. The solution is obtained using finite integral transformation technique and is the sum of two uniformly and absolutely convergent power series.
Keywords
Hyperbolic equations, initial boundary value problems
First Page
317
Last Page
324
Recommended Citation
DERNEK, Neşe (1997) "On The Solution of the E.P.D. Equation Using Finite Integral Transformations," Turkish Journal of Mathematics: Vol. 21: No. 3, Article 8. Available at: https://journals.tubitak.gov.tr/math/vol21/iss3/8
