- AutorIn
- Tuan Anh Dao Hanoi University of Science and Technology#Technische Universität Bergakademie Freiberg
- Titel
- Global in time existence of Sobolev solutions to semi-linear damped sigma-evolution equations in L^q scales
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:105-qucosa2-716493
- Datum der Einreichung
- 04.05.2020
- Datum der Verteidigung
- 04.08.2020
- Abstract (EN)
- The main goal of this thesis is to prove the global (in time) existence of small data Sobolev solutions to semi-linear damped σ-evolution equations from suitable function spaces basing on L^q spaces by mixing additional L^m regularity for the data on the basis of L^q-L^q estimates for solutions, with q∈(1,∞) and m∈[1,q), to the corresponding linear models. To establish desired results, we would like to apply the theory of modified Bessel functions, Faà di Bruno's formula and Mikhlin-Hörmander multiplier theorem in the treatment of linear problems. In addition, some of modern tools from Harmonic Analysis play a fundamental role to investigate results for the global existence of small data Sobolev solutions to semi-linear problems. Finally, the application of a modified test function method is to devote to the proof of blow-up results for semi-linear damped σ-evolution models, where σ≥1 and δ∈[0,σ) are assumed to be any fractional numbers.
- Freie Schlagwörter (EN)
- sigma-evolution equations, damping terms, L^1 estimates, global existence, blow-up
- Klassifikation (DDC)
- 510
- Normschlagwörter (GND)
- Evolutionsgleichung
- Cauchy-Anfangswertproblem
- GutachterIn
- Prof. Dr. Michael Reissig
- Prof. Dr. Marcelo Ebert
- Prof. Dr. Rainer Picard
- BetreuerIn Hochschule / Universität
- Prof. Dr. Michael Reissig
- Verlag
- TU Bergakademie Freiberg, Freiberg
- Den akademischen Grad verleihende / prüfende Institution
- TU Bergakademie, Freiberg
- Version / Begutachtungsstatus
- publizierte Version / Verlagsversion
- URN Qucosa
- urn:nbn:de:bsz:105-qucosa2-716493
- Veröffentlichungsdatum Qucosa
- 15.09.2020
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch
- Lizenz / Rechtehinweis