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pde_system [2013/09/16 22:54] nikolaj |
pde_system [2013/09/17 09:34] nikolaj |
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| | @#88DDEE: $ \alpha $ ... sequence of length $n$ of multi-indices | | | @#88DDEE: $ \alpha $ ... sequence of length $n$ of multi-indices | | ||
| | @#88DDEE: $ F:\mathbb R^D\times\mathbb R^{d\ \cdot\ (1+n)}\to \mathbb R^m $ | | | @#88DDEE: $ F:\mathbb R^D\times\mathbb R^{d\ \cdot\ (1+n)}\to \mathbb R^m $ | | ||
| - | | @#88DDEE: $ B:\mathbb R^d\to \mathbb R^k $ | | ||
| - | | @#FFBB00: $ u $ | | + | | @#FFBB00: $ u \in \mathrm{it} $ | |
| | @#55EE55: $u:C^k(\mathbb R^D,\mathbb R^d) $ | | | @#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 $ | | | @#55EE55: $ F(x,u(x),u^{(\alpha_1)}(x),u^{(\alpha_2)}(x),\dots,u^{(\alpha_n)}(x))=0 $ | | ||
| - | | @#55EE55: $ B(u)=0 $ | | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
