Brandt, Felix Christopher Helmut Ludwig (2024)
Geophysical Flow Models: An Approach by Quasilinear Evolution Equations.
Technische Universität Darmstadt
doi: 10.26083/tuprints-00027378
Dissertation, Erstveröffentlichung, Verlagsversion
Kurzbeschreibung (Abstract)
This thesis develops rigorous analysis of geophysical flow models in the context of Hibler's viscous-plastic sea ice model by means of quasilinear evolution equations. In a first step, well-posedness results for a fully parabolic variant are shown. Another focal point is the interaction problem of sea ice with a rigid body. Moreover, a coupled atmosphere-sea ice-ocean model is analyzed from a rigorous mathematical point of view. The first part of the thesis is completed by the local strong well-posedness of a parabolic-hyperbolic variant of Hibler's model. In the second part of the thesis, frameworks to quasilinear time periodic evolution equations are presented. One approach relies on maximal periodic regularity and the Arendt-Bu theorem, whereas the other one is based on the classical Da Prato-Grisvard theorem. Finally, applications of these frameworks to Hibler's sea ice model, Keller-Segel systems as well as a Nernst-Planck-Poisson type system are provided.
| Typ des Eintrags: | Dissertation | ||||
|---|---|---|---|---|---|
| Erschienen: | 2024 | ||||
| Autor(en): | Brandt, Felix Christopher Helmut Ludwig | ||||
| Art des Eintrags: | Erstveröffentlichung | ||||
| Titel: | Geophysical Flow Models: An Approach by Quasilinear Evolution Equations | ||||
| Sprache: | Englisch | ||||
| Referenten: | Hieber, Prof. Dr. Matthias ; Egert, Prof. Dr. Moritz ; Kozono, Prof. Dr. Hideo | ||||
| Publikationsjahr: | 27 Mai 2024 | ||||
| Ort: | Darmstadt | ||||
| Kollation: | xxviii, 314 Seiten | ||||
| Datum der mündlichen Prüfung: | 15 Mai 2024 | ||||
| DOI: | 10.26083/tuprints-00027378 | ||||
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/27378 | ||||
| Kurzbeschreibung (Abstract): | This thesis develops rigorous analysis of geophysical flow models in the context of Hibler's viscous-plastic sea ice model by means of quasilinear evolution equations. In a first step, well-posedness results for a fully parabolic variant are shown. Another focal point is the interaction problem of sea ice with a rigid body. Moreover, a coupled atmosphere-sea ice-ocean model is analyzed from a rigorous mathematical point of view. The first part of the thesis is completed by the local strong well-posedness of a parabolic-hyperbolic variant of Hibler's model. In the second part of the thesis, frameworks to quasilinear time periodic evolution equations are presented. One approach relies on maximal periodic regularity and the Arendt-Bu theorem, whereas the other one is based on the classical Da Prato-Grisvard theorem. Finally, applications of these frameworks to Hibler's sea ice model, Keller-Segel systems as well as a Nernst-Planck-Poisson type system are provided. |
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| Alternatives oder übersetztes Abstract: |
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| Status: | Verlagsversion | ||||
| URN: | urn:nbn:de:tuda-tuprints-273780 | ||||
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik | ||||
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Analysis 04 Fachbereich Mathematik > Analysis > Angewandte Analysis |
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| Hinterlegungsdatum: | 27 Mai 2024 12:01 | ||||
| Letzte Änderung: | 03 Jun 2024 11:49 | ||||
| PPN: | |||||
| Referenten: | Hieber, Prof. Dr. Matthias ; Egert, Prof. Dr. Moritz ; Kozono, Prof. Dr. Hideo | ||||
| Datum der mündlichen Prüfung / Verteidigung / mdl. Prüfung: | 15 Mai 2024 | ||||
| Export: | |||||
| Suche nach Titel in: | TUfind oder in Google | ||||
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