Now it's clear as DAE!

Differential-Algebraic Equations (DAEs) are a class of mathematical models that combine differential and algebraic equations. They are widely used to model a variety of real-world systems, including mechanical systems, electrical circuits, chemical engineering and control systems. While finite-dimensional DAEs have been extensively studied, infinite-dimensional DAEs present unique challenges, particularly in terms of their index. The Applied Mathematics Group (Caren Tischendorf) has delved into the intricacies of these index concepts in the context of both finite-dimensional and infinite-dimensional linear DAEs. Find out more in their DAE Panel Article!

Abstract

Different index concepts for regular linear differential-algebraic equations are defined and compared in the general Banach space setting. For regular finite dimensional linear differential-algebraic equations, all these indices exist and are equivalent. For infinite dimensional systems, the situation is more complex. It is proven that although some indices imply others, in general they are not equivalent. The situation is illustrated with a number of examples.