Index Concepts for Linear Differential-Algebraic Equations in Infinite Dimensions
DOI:
https://doi.org/10.52825/dae-p.v2i.2514Keywords:
Differential-Algebraic Equations, Index, Partial Differential Equations, Functional AnalysisAbstract
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.
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Copyright (c) 2024 Mehmet Erbay, Birgit Jacob, Kirsten Morris, Timo Reis, Caren Tischendorf
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