# Reis 2007 March 8

### From NA-Wiki

**Speaker:** Dr. Timo Reis, Technical University Berlin.

**Title:** Abstract Differential-Algebraic Equations - An Overview.

**When:** The NA seminar meets om Wed March 8 at 15:15 in D4523

**Abstract**

Rewriting partial differential equations containing time derivatives as ordinary differential equations in infinite dimensional Banach spaces is a convenient technique in their analysis. In an analogous way, coupled systems of differential-algebraic equations and partial differential equations (or also called "partial differential-algebraic equations") can be formulated as differential-algebraic systems on infinite dimensional spaces. Motivated by the case of (finite dimensional) differential-algebraic equations, we will consider generalizations of basic tools like the Kronecker normal form to infinite dimensions. Based on these results, we can parametrize the set of consistent initial values and further, the sensitivity of solutions with respect to perturbations of the given data can be measured. The results are illustrated by concrete examples from engineering, such as delay-differential equations and electrical circuits with transmission lines.