Cauchy Problem
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
conditions.
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