cauchy problem

Fetched 2026-10-26 (cache).

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Noun

1. {{lb|en|mathematics|analysis}} For a given ''m''-order [[partial differential equation]], the problem of finding a solution function <math>u</math> on <math>\mathbb{R}^n</math> that satisfies the boundary conditions that, for a [[smooth manifold]] <math>S\subset\mathbb{R}^n</math>, <math>\textstyle u(x) = f_0(x)</math> and <math>\textstyle \frac{\partial^k u(x)}{\partial n^k} = f_k(x)</math>, <math>\forall x\in S</math>, <math> k = 1\dots m-1</math>, given specified functions <math>f_k</math> defined on, and [[vector]] <math>n</math> [[normal]] to, the manifold.

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