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.
ORCID iDs
Trostorff, Sascha and Waurick, Marcus ORCID: https://orcid.org/0000-0003-4498-3574;-
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Item type: Article ID code: 65895 Dates: DateEvent5 January 2019Published23 July 2018Published Online12 June 2018AcceptedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 30 Oct 2018 15:20 Last modified: 31 Oct 2024 01:44 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/65895