On a method of solving the initial value problem for the wave equation
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- by Tosihusa Kimura and Yasutaka Sibuya PDF
- Proc. Amer. Math. Soc. 50 (1975), 205-215 Request permission
Abstract:
The wave equation is formally reduced to Laplace’s equation by the change of variable ${x_0} = it$, where $i = \sqrt { - 1}$. In this paper we shall derive the well-known formula for the solution of Cauchy’s problem of the wave equation from the integral representations of the solutions of Dirichlet and Neumann problems of Laplace’s equation in the half-plane. Our method can be viewed as a hyperfunction-theoretic approach.References
- P. R. Garabedian, Partial differential equations with more than two independent variables in the complex domain, J. Math. Mech. 9 (1960), 241–271. MR 0120441, DOI 10.1512/iumj.1960.9.59015
- P. R. Garabedian, Partial differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0162045
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 205-215
- MSC: Primary 35C15; Secondary 35L05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0369879-1
- MathSciNet review: 0369879