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pde_system [2013/09/17 09:34] nikolaj |
pde_system [2015/03/27 20:14] nikolaj |
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| ===== PDE system ===== | ===== PDE system ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $ D,d,n,m,k\in\mathbb N $ | | + | | @#55CCEE: context | @#55CCEE: $ D,d,n,m,k\in\mathbb N $ | |
| - | | @#88DDEE: $ \alpha $ ... sequence of length $n$ of multi-indices | | + | | @#55CCEE: context | @#55CCEE: $ \alpha $ ... sequence of length $n$ of multi-indices | |
| - | | @#88DDEE: $ F:\mathbb R^D\times\mathbb R^{d\ \cdot\ (1+n)}\to \mathbb R^m $ | | + | | @#55CCEE: context | @#55CCEE: $ F:\mathbb R^D\times\mathbb R^{d\ \cdot\ (1+n)}\to \mathbb R^m $ | |
| + | | @#FFBB00: definiendum | @#FFBB00: $ u \in \mathrm{it} $ | | ||
| + | | @#55EE55: postulate | @#55EE55: $u:C^k(\mathbb R^D,\mathbb R^d) $ | | ||
| + | | @#55EE55: postulate | @#55EE55: $ F(x,u(x),u^{(\alpha_1)}(x),u^{(\alpha_2)}(x),\dots,u^{(\alpha_n)}(x))=0 $ | | ||
| - | | @#FFBB00: $ u \in \mathrm{it} $ | | + | ----- |
| - | + | ||
| - | | @#55EE55: $u:C^k(\mathbb R^D,\mathbb R^d) $ | | + | |
| - | + | ||
| - | | @#55EE55: $ F(x,u(x),u^{(\alpha_1)}(x),u^{(\alpha_2)}(x),\dots,u^{(\alpha_n)}(x))=0 $ | | + | |
| - | + | ||
| - | ==== Discussion ==== | + | |
| - | ==== Parents ==== | + | |
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Partial_differential_equation|Partial differential equation]] | Wikipedia: [[http://en.wikipedia.org/wiki/Partial_differential_equation|Partial differential equation]] | ||
| + | |||
| + | ----- | ||
| === Refinement of === | === Refinement of === | ||
| [[Monoid kernel]] | [[Monoid kernel]] | ||
| - | === Requirements === | + | === Context === |
| [[Fréchet derivative]], [[Multi-index power]] | [[Fréchet derivative]], [[Multi-index power]] | ||
