On differential–algebraic equations in infinite dimensions

Trostorff, Sascha and Waurick, Marcus (2019) On differential–algebraic equations in infinite dimensions. Journal of Differential Equations, 266 (1). pp. 526-561. ISSN 0022-0396 (https://doi.org/10.1016/j.jde.2018.07.051)

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Abstract

We consider a class of differential–algebraic equations (DAEs) with index zero in an infinite dimensional Hilbert space. We define a space of consistent initial values, which lead to classical continuously differential solutions for the associated DAE. Moreover, we show that for arbitrary initial values we obtain mild solutions for the associated problem. We discuss the asymptotic behaviour of solutions for both problems. In particular, we provide a characterisation for exponential stability and exponential dichotomies in terms of the spectrum of the associated operator pencil.

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