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Dissertation
Analysis for periodic traveling interfacial hydroelastic waves
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2018
DOI:
https://doi.org/10.17918/D8VM1R
Abstract
We prove two bifurcation theorems for the existence of spatially periodic traveling waves in an elastic sheet between two two-dimensional fluids of infinite depth. We allow for zero or positive mass along the sheet, and treat both cases in a unified way. Our first main result is a global bifurcation theorem; we apply to this traveling hydroelastic wave problem an abstract theorem regarding bifurcation via odd crossing number. This theorem requires the relevant mapping's linearization to have one-dimensional kernel; however, there are certain parameter values at which a two-dimensional kernel is achieved. Our second main result, which makes use of an implicit function theorem argument, is a bifurcation theorem for traveling wave solutions in these cases of two-dimensional kernel. We also present an asymptotic study of Wilton ripples, which are traveling waves that occur in particular cases of a two-dimensional kernel.
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Details
- Title
- Analysis for periodic traveling interfacial hydroelastic waves
- Creators
- Davia W. Sulon - Drexel University, Mathematics
- Contributors
- David M. Ambrose (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- ix, 87 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 7917; 991014632683204721