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On a method of solving the initial value problem for the wave equation


Authors: Tosihusa Kimura and Yasutaka Sibuya
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
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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 [Enhancements On Off] (What's this?)

  • [1] P. R. Garabedian, Partial differential equations with more than two independent variables in the complex domain, J. Math. Mech. 9 (1960), 241-271. MR 22 #11195. MR 0120441 (22:11195)
  • [2] -, Partial differential equations, Wiley, New York, 1964. MR 28 #5247. MR 0162045 (28:5247)

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DOI: https://doi.org/10.1090/S0002-9939-1975-0369879-1
Article copyright: © Copyright 1975 American Mathematical Society

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