Cauchy-Kovalevskaya Theorem

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.")

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.