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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0369879-1
PII: S 0002-9939(1975)0369879-1
Article copyright: © Copyright 1975 American Mathematical Society