Index Concepts for Linear Differential-Algebraic Equations in Infinite Dimensions
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.
Authors
- Timo Reis (ORCID: https://orcid.org/0000-0003-0721-8494)
- Caren Tischendorf (ORCID: https://orcid.org/0000-0002-8421-7199)
- Kirsten Morris (ORCID: https://orcid.org/0000-0003-1311-9230)
- Birgit Jacob (ORCID: https://orcid.org/0000-0002-8775-4424)
- Mehmet Erbay (ORCID: https://orcid.org/0009-0007-1214-2929)
Institutions
- Technische Universität Ilmenau (DE)
- University of Waterloo (CA)
- University of Wuppertal (DE)
- Humboldt-Universität zu Berlin (DE)
Publication Details
- Journal
- DAE Panel
- Published
- 2024-10-24
- DOI
- https://doi.org/10.52825/dae-p.v2i.2514
- Citations
- 5
- Primary Topic
- Numerical methods for differential equations
- Type
- article
- Field-Weighted Citation Impact
- 3.66