The solution of Cauchy's Problem for linear partial differential equations, with constant coefficients, by means of integrals involving complex variables
- 1 May 1927
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 1 (2) , 94-103
- https://doi.org/10.1017/s0013091500007410
Abstract
The object of this paper is to show how the theory of integrals involving complex variables may be applied to the integration of linear partial differential equations, possessing real, distinct characteristics and constant coefficients. The problem considered is a Cauchy problem (with analytic data)—typical of the equation of real characteristics and the method taken is that of Riemann. For simplicity of exposition, the second order hyperbolic equation is considered, but the results are given in such a form as to indicate an obvious generalisation to equations of higher order.Keywords
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