PDE system

Set

context $ D,d,n,m,k\in\mathbb N $
context $ \alpha $ … sequence of length $n$ of multi-indices
context $ F:\mathbb R^D\times\mathbb R^{d\ \cdot\ (1+n)}\to \mathbb R^m $
definiendum $ u \in \mathrm{it} $
postulate $u:C^k(\mathbb R^D,\mathbb R^d) $
postulate $ F(x,u(x),u^{(\alpha_1)}(x),u^{(\alpha_2)}(x),\dots,u^{(\alpha_n)}(x))=0 $

Reference

Wikipedia: Partial differential equation


Refinement of

Monoid kernel

Context

Fréchet derivative, Multi-index power