Preprint 17-2013

Analysis of linear variable coefficient delay differential-algebraic equations

Author(s) : Phi Ha , Volker Mehrmann , Andreas Steinbrecher

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 17-2013

MSC 2000

34A09 Implicit equations, differential-algebraic equations

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

Abstract :
The analysis of general linear variable coefficient delay differential-algebraic systems (DDAEs) is presented. The solvability for DDAEs is investigated and a reformulation procedure to regularize a given DDAE is developed. Based on this regularization procedure existence and uniqueness of solutions and consistency of initial functions is analyzed as well as other structural properties of DDAEs like smoothness requirements. We also present some examples to demonstrate that for the numerical solution of a DDAE, a reformulation of the system before applying numerical methods is essential.

Keywords : Differential-algebraic equation, delay differential-algebraic equation, regularization, existence of solutions, uniqueness of solutions, consistency conditions