===== PDE system =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $ D,d,n,m,k\in\mathbb N $ |
| @#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 $ |
| @#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 $ |

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=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Partial_differential_equation|Partial differential equation]]

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=== Refinement of ===
[[Monoid kernel]]
=== Context ===
[[Fréchet derivative]], [[Multi-index power]]