Cauchy problem

English

Etymology

After French mathematician Template:W.

Noun

1. Template:Lb For a given m-order partial differential equation, the problem of finding a solution function $u$ on ${ℝ}^n$ that satisfies the boundary conditions that, for a smooth manifold $S\subset {ℝ}^n$, $u(x)=f_0(x)$ and $\frac{{\partial }^{k}u(x)}{\partial n^k}=f_k(x)$, $\mathrm{\forall }x\in S$, $k=1\dots m-1$, given specified functions $f_k$ defined on, and vector $n$ normal to, the manifold.
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Usage notes

The hypersurface S is called the Template:M. The functions f_k defined on S are collectively known as the Template:M of the problem.

Translations

• Italian: Template:T

Further reading

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