A procedure following the theory of Pomander is explained for finding the fundamental solution to a hyperbolic linear partial differential equation with constant coefficients. The relevant theorems concerning hyperbolic operators are reviewed and the fundamental solutions are derived for the one and the two dimensional wave equations, and for the equation of small disturbances propagating in a uniform subsonic or supersonic stream. By means of these examples, it is demonstrated that Hormone’s theory provides a clear and valuable procedure for obtaining the fundamental solution and for defining the region of integration of the convolution integral solution to the inhomogeneous partial differential equation. By the appropriate choice of inhomogeneous term, the solution to the Cauchy problem for the plane of initial time is easily found for each of the three partial differential equations considered.
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