A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain. A Cauchy problem may involve initial or boundary values. It is named after Augustin-Louis Cauchy.

Formal statement

and a smooth manifold is called the Cauchy surface that satisfies,

(collectively known as the Cauchy data of the problem). The derivative of order zero means that the function itself is specified.

Cauchy–Kowalevski theorem

The Cauchy–Kovalevskaya theorem, named in honor of Cauchy and Sofya Kovalevskaya are analytic.

See also

• Cauchy boundary condition

• Cauchy horizon

References

Further reading

• Hille, Einar (1956)[1954]. Some Aspect of Cauchy's Problem Proceedings of 1954 ICM vol III section II (analysis half-hour invited address) p.1 0 9 ~ 1 6.

• Sigeru Mizohata(溝畑 茂 1965). Lectures on Cauchy Problem. Tata Institute of Fundamental Research.

• Sigeru Mizohata (1985).On the Cauchy Problem. Notes and Reports in Mathematics in Science and Engineering. 3. Academic Press, Inc.. ISBN 9781483269061

• Arendt, Wolfgang; Batty, Charles; Hieber, Matthias; Neubrander, Frank (2001), Vector-valued Laplace Transforms and Cauchy Problems, Birkhauser.

External links

• Cauchy problem at MathWorld.

de:Anfangswertproblem#Partielle Differentialgleichungen