This theorem states that, for a partial differential equation involving a time derivative of order 
, the solution is uniquely determined if time derivatives up
to order 
of the dependent variable are specified at a single surface, provided the surface
is a free surface i.e., not a characteristic surface. (In wave problems, a characteristic
surface is the same as a wavefront. In problems of dimension greater than three,
replace "surface" with "hypersurface.")
Cauchy-Kovalevskaya Theorem
See also
Boundary Conditions, Cauchy Conditions, Cauchy Problem, Partial Differential EquationExplore with Wolfram|Alpha
References
Courant, R. and Hilbert, D. Methods of Mathematical Physics, Vol. 1. New York: Wiley, 1989.Courant, R. and Hilbert, D. Methods of Mathematical Physics, Vol. 2. New York: Wiley, 1989.Referenced on Wolfram|Alpha
Cauchy-Kovalevskaya TheoremCite this as:
Weisstein, Eric W. "Cauchy-Kovalevskaya Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cauchy-KovalevskayaTheorem.html