On the solution of the E.P.D. equation using finite integral transformations

Abstract

In this paper, a solution is given for the following initial boundary value problem: k Δu = utt + -tkut + g(x, t) (t > 0) u(0, t) = u(a, t) = 0 u(x, 0) = f(x), ut(x, 0) = 0 where x, a ∈ Rn, t is the time variable, k < 1, k ≠ -1, -2, -3, . . . is a real parameter, Δ 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. © TÜBİTAK.