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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Abstract differential-algebraic equations
verfasst von : René Lamour, Roswitha März, Caren Tischendorf
Erschienen in: Differential-Algebraic Equations: A Projector Based Analysis
Verlag: Springer Berlin Heidelberg
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The concept of regular DAEs developed in Part I for DAEs in finite-dimensional spaces is generalized to some extend for DAEs acting in Hilbert spaces, which are called abstract differential-algebraic equations (ADAEs). Such a framework aims to provide a systematic approach for coupled systems of different type. It should be emphasized that this working field is still in its infancy and further research is absolutely reasonable. After having discussed various special cases we turn to a class of linear ADAEs which covers parabolic PDEs and index-1 DAEs as well as couplings thereof. We treat this class in detail by means of Galerkin methods yielding an existence and uniqueness result for the ADAE as well as an error estimation for the perturbed systems.