- Titel
- Quantified Tauberian Theorems and Applications to Decay of Waves
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa-232101
- Datum der Einreichung
- 15.09.2017
- Datum der Verteidigung
- 04.12.2017
- Abstract (EN)
- The thesis consists of two parts, a theoretical part and an applied part, and in addition an Appendix. Except for a very short chapter in the applied part and the appendix we only present previously unknown results leading to a very concise style. In the theoretical part we study rates of decay for vector-valued functions and semigroups of operators depending on a real and positive variable. Under boundedness assumptions on the function/semigroup itself and under analytic extendability assumptions of its Laplace transform/resolvent across the imaginary axis we provide (almost) sharp rates of decay. Our results improve known results in this very active area of research. In the second part of the thesis we apply our results to specific examples (from the field of PDEs): local energy decay for wave equations on exterior domains, energy decay for damped wave equations on bounded domains and decay for a viscoelastic boundary damping model for sound waves. Many more examples can be found in the vast literature.
- Freie Schlagwörter (DE)
- C0-Halbgruppe, Abklingrate, Gedämpfte Wellengleichung, Resolventenabschätzung
- Freie Schlagwörter (EN)
- C0-Semigroup, rates of decay, damped wave equation, resolvent estimate
- Klassifikation (DDC)
- 510
- Klassifikation (RVK)
- SK 450
- GutachterIn
- Prof. Dr. Ralph Chill
- Prof. Dr. Charles Batty
- BetreuerIn
- Prof. Dr. Ralph Chill
- Den akademischen Grad verleihende / prüfende Institution
- Technische Universität Dresden, Dresden
- URN Qucosa
- urn:nbn:de:bsz:14-qucosa-232101
- Veröffentlichungsdatum Qucosa
- 18.01.2018
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch
- Lizenz / Rechtehinweis
- Inhaltsverzeichnis
Part 1 Quantified Tauberian theorems and decay of C0-semigroups 1 Decay of vector-valued functions 2 Optimal decay for C0-semigroups on Hilbert spaces Part 2 Applications: decay of waves 3 Local decay for waves in exterior domains 4 Waves on a square with constant damping on a strip 5 A viscoelastic boundary damping model