Differences
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pde_system [2014/03/21 11:11] 127.0.0.1 external edit |
pde_system [2015/03/27 20:14] nikolaj |
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| @#55CCEE: context | @#55CCEE: $ \alpha $ ... sequence of length $n$ of multi-indices | | | @#55CCEE: context | @#55CCEE: $ \alpha $ ... sequence of length $n$ of multi-indices | | ||
| @#55CCEE: context | @#55CCEE: $ 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 $ | | ||
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| @#FFBB00: definiendum | @#FFBB00: $ u \in \mathrm{it} $ | | | @#FFBB00: definiendum | @#FFBB00: $ u \in \mathrm{it} $ | | ||
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| @#55EE55: postulate | @#55EE55: $u:C^k(\mathbb R^D,\mathbb R^d) $ | | | @#55EE55: postulate | @#55EE55: $u:C^k(\mathbb R^D,\mathbb R^d) $ | | ||
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| @#55EE55: postulate | @#55EE55: $ F(x,u(x),u^{(\alpha_1)}(x),u^{(\alpha_2)}(x),\dots,u^{(\alpha_n)}(x))=0 $ | | | @#55EE55: postulate | @#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]] | ||
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=== Refinement of === | === Refinement of === | ||
[[Monoid kernel]] | [[Monoid kernel]] | ||
=== Context === | === Context === | ||
[[Fréchet derivative]], [[Multi-index power]] | [[Fréchet derivative]], [[Multi-index power]] |