If is an Analytic Function in a Neighborhood of the point (i.e., it can be expanded in
a series of Nonnegative Integer Powers of and ), find a solution
of the Differential Equation

with initial conditions and . The existence and uniqueness of the solution were proven by Cauchy and Kovalevskaya in the Cauchy-Kovalevskaya Theorem. The Cauchy problem amounts to determining the shape of the boundary and type of equation which yield unique and reasonable solutions for the Cauchy Boundary Conditions.

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1999-05-26