SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Solvability analysis and reformulation of general Linear Delay Differential-Algebraic Equations

P. Ha, V. Mehrmann and A. Steinbrecher

Abstract
Delay differential equations (DDEs) arise in a variety of applications, including physical systems, biological systems and electronic networks. If the states of the physical system are constrained, e.g., by conservation laws or interface conditions, or some economical interest are involved in the biological model, then algebraic equations have to be included and one has to analyze delay differential-algebraic equations (Delay-DAEs). In this talk, we present our recent result on the solvability analysis of general linear Delay-DAEs, i.e., systems with linear time variable coefficients. We propose the method to reformulate a Delay-DAE into its underlying delay system, which can be used to address structural properties of the system like existence and uniqueness of a solution, consistency and smoothness requirements. We also consider some spectral properties of Linear Delay-DAEs and their relations to the solvability analysis of the system.

Bibliography
[1] P. Ha, V. Mehrmann and A. Steinbrecher, Analysis of linear variable coefficient delay differential-algebraic equations Preprint 17/2013, Institut für Mathematik, TU Berlin, 2013.
[2] P. Ha and V. Mehrmann, Analysis and Reformulation of Linear Delay Differential-Algebraic Equations, Electron. J. Linear Algebra, 23:703-730, 2012.

Organized by         Universidad de Valladolid     IMUVA