Englisch-Finnisch Übersetzung für cauchy problem

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

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