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Cauchy-Kovalevskaya 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.")


See also

Boundary Conditions, Cauchy Conditions, Cauchy Problem, Partial Differential Equation

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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.

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Cauchy-Kovalevskaya Theorem

Cite this as:

Weisstein, Eric W. "Cauchy-Kovalevskaya Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cauchy-KovalevskayaTheorem.html

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