In this thesis, we are interested in damped wave models with time-dependent propagation speed and time-dependent damping term both having a time-dependent oscillation term. The main goal of this thesis is to understand the influence of strong time-dependent oscillations on Sobolev solutions to the linear models and consequently, to the semilinear models. Especially, due to the deteriorating influence of oscillations on solutions, a stabilization condition and higher-order regularity of the time-dependent coefficients may compensate 'bad behaviors' arising from oscillations.:1. Introduction
2. The influence of oscillations on linear damped wave equation with time-dependent coefficients
3. Global in time existence results for damped wave models with power nonlinearity
4. Global in time existence results for damped wave models with different power nonlinearities
5. Lp-Lq estimates for wave equations with strong time-dependent oscillations
6. Further research topics
A. Basic tools
B. List of symbols and abbreviations
Bibliography
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:71000 |
| Date | 14 July 2020 |
| Creators | Aslan, Halit Sevki |
| Contributors | Reissig, Michael, Hirosawa, Fumihiko, Picard, Rainer, Bernstein, Swanhild, Hebisch, Udo, Starkloff, Hans-Jörg, TU Bergakademie Freiberg |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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