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.
