Cauchy-Kowalewska existence theorem

This theorem states that, for a partial differential equation involving a time derivative of order n, the solution is uniquely determined if time derivatives up to order n - 1 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.")

boundary conditions | Cauchy conditions | Cauchy problem | partial differential equation