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  5. Διατριβές Μεταπτυχιακής Έρευνας (Masters) - ΜΑΘ
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Please use this identifier to cite or link to this item: https://olympias.lib.uoi.gr/jspui/handle/123456789/39164
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dc.contributor.authorΖυγόρη, Μαρίαel
dc.contributor.authorZygori, Maria
dc.date.accessioned2025-07-07T10:50:26Z-
dc.date.available2025-07-07T10:50:26Z-
dc.identifier.urihttps://olympias.lib.uoi.gr/jspui/handle/123456789/39164-
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/us/*
dc.subjectΕξίσωση υδάτινων κυμάτωνel
dc.subjectΠρόβλημα ελεύθερης επιφάνειαςel
dc.subjectΣτάσιμα περιοδικά οδεύοντα κύματαel
dc.subjectΣτροβιλισμόςel
dc.subjectΘεωρία τοπικής διακλάδωσης (Θεώρημα Crandall-Rabinowitz)el
dc.titleΠεριοδικά υδάτινα κύματα υπό την παρουσία στροβιλισμούel
dc.titlePeriodic water waves under the presence of vorticityen
dc.typemasterThesis-
heal.typemasterThesisel
heal.type.enMaster thesisen
heal.type.elΜεταπτυχιακή εργασίαel
heal.dateAvailable2025-07-07T10:51:26Z-
heal.languageelel
heal.accessfreeel
heal.recordProviderΠανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημώνel
heal.publicationDate2025-07-07-
heal.abstractΣτην εργασία αποδεικνύεται η ύπαρξη σταθερών περιοδικών οδευόντων υδάτινων κυμάτων πεπερασμένου βάθους υπό την επίδραση της βαρύτητας και υπό την παρουσία στροβιλισμού, τα οποία είναι μη τετριμμένα και έχουν μικρό πλάτος, αλλά συγκεκριμένη μορφή και στηρίχθηκε στο άρθρο των Constantin A., Strauss W.: Exact Steady Periodic Water Waves with Vorticity, Comm. PureAppl. Math. 57, 481527, 2004 καθώς και στο βιβλίο του Constantin A.: Nonlinear water waves with applications to wave-currents interactions and tsunamis, SIAM,2011.el
heal.abstractThe subject matter of the present thesis is the application of a result of local bifurcation theory, a sub eld of Nonlinear Functional Analysis, to a problem for water waves. More precisely, in the thesis it is proven that there exist steady periodic traveling water waves of nite depth due to the impact of gravity and under the presence of vorticity, which are non-trivial and of small amplitude, but of a certain form. In the rst chapter, at rst the problem and the obtained result are pre- sented. Then, this problem, which is initially a free boundary problem, is transformed into a problem over a xed bounded domain for a quasi-linear el- liptic partial di erential equation of second order which has partly non-linear rst order boundary conditions. In the second chapter, at rst it is proven that there exists a one-parametric family of trivial solutions of the problem. Then, the problem is translated into the language of suitable spaces and operators and the Crandall-Rabinowitz Theorem of local bifurcation theory is applied in order to prove that from a certain value of this parameter bifurcates a curve of non-trivial solutions. The second chapter is completed with a study of the form of these solutions. This thesis was based on the article Constantin A., Strauss W.: Exact Steady Periodic Water Waves with Vorticity, Comm. PureAppl. Math. 57, 481 527, 2004 [3] and the book Constantin A.: Nonlinear water waves with applications to wave-currents interactions and tsunamis, SIAM, 2011 [5]en
heal.advisorNameΓιαννούλης, Ιωάννηςel
heal.committeeMemberNameΠουρναράς, Ιωάννηςel
heal.committeeMemberNameΜαυρίδης, Κυριάκοςel
heal.committeeMemberNameΓιαννούλης, Ιωάννηςel
heal.academicPublisherΠανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικώνel
heal.academicPublisherIDuoiel
heal.numberOfPages66el
heal.fullTextAvailabilitytrue-
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