Werner M. Seiler: "Completion to involution and the numerical integration of general systems of PDEs"
Lehrstuhl Mathematik I
Universität Mannheim

We discuss some properties of involutive systems of partial differential equations and how they affect their numerical integration. This includes a bit of existence and perturbation theory, index concepts as they are very popular for (partial) differential algebraic equations, and an analysis of semi-discretisations. The emphasis is not on obtaining the strongest possible results but on demonstrating how ideas from the theory of involutive systems allow us to "lift" (sometimes very easily) results on systems in Cauchy-Kovalevskaya form to over-determined systems.