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Spiral Waves in Circular and Spherical Geometries
Dai, Jia-Yuan

HaupttitelSpiral Waves in Circular and Spherical Geometries
TitelzusatzThe Ginzburg-Landau Paradigm
TitelvarianteSpiralwellen in der Kreisgeometrie und der sphärischen Geometrie
Zusatz zur TitelvarianteDas Ginzburg-Landau Paradigma
AutorDai, Jia-Yuan
Geburtsort: Taichung, Taiwan
GutachterProf. Dr. Bernold Fiedler
weitere GutachterProf. Dr. Chen Chiun-Chuan
Freie Schlagwörtercomplex Ginzburg-Landau equation; spiral waves; circular geometry; spherical geometry; 2-tip spirals; global bifurcation
DDC515 Analysis
ZusammenfassungIn this thesis we establish a functional approach to prove the existence of Ginzburg-Landau spiral waves. Based on systematic considerations, we justify the popular m-armed spiral Ansatz by equivariance and the variational structure of the real Ginzburg-Landau equation. This spiral Ansatz transforms the Ginzburg-Landau equation into an elliptic equation. To solve this elliptic equation by our functional approach, we adopt global bifurcation analysis and the result of existence is essentially a consequence of compactness.
The advantage of our functional approach is threefold. First, it avoids smart, but tricky, estimates used in the shooting method. Second, it works for more general underlying spatial domains, not only in the circular geometry, but also in the spherical geometry. Third, it permits the occurrence of a mixed diffusion process when a complex diffusion parameter is introduced. Thus our result of existence of rigidly-rotating spiral waves greatly generalizes those in the literature. Moreover, we prove the existence of two new patterns: frozen spirals in circular and spherical geometries, and 2-tip spirals in the spherical geometry.
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Seitenzahliv, 86 Seiten
Fachbereich/EinrichtungFB Mathematik und Informatik
Erscheinungsjahr2017
Dokumententyp/-SammlungenDissertation
Medientyp/FormatText
SpracheEnglisch
Rechte Nutzungsbedingungen
Tag der Disputation13.07.2017
Erstellt am20.09.2017 - 14:30:47
Letzte Änderung22.09.2017 - 11:34:31
 
Statische URLhttp://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000105545
URNurn:nbn:de:kobv:188-fudissthesis000000105545-5
Zugriffsstatistik
E-Mail-Adressentutiws@gmail.com