The thesis deals with so-called evolutionary equations, a class of abstract linear operator equations, which cover a huge class of partial differential equation with and without memory. We provide a unified Hilbert space framework for the well-posedness of such equations. Moreover, we inspect the exponential stability of those problems and construct spaces of admissible inital values and pre-histories, on which a strongly continuous semigroup could be associated with the given problem. The theoretical results are illustrated by several examples.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:14-qucosa-236494 |
| Date | 31 May 2018 |
| Creators | Trostorff, Sascha |
| Contributors | Technische Universität Dresden, Fakultät Mathematik und Naturwissenschaften, Prof. Dr. Ralph Chill |
| Publisher | Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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