On some Nonlinear Aspects of Wave Motion
(2005)- Abstract
- In the first part of this thesis we consider the governing equations for capillary water waves given by the Euler equations with a free surface under the influence of surface tension over a flat bottom. We look for two-dimensional steady periodic waves. The problem is first transformed to a nonlinear elliptic equation in a rectangle. Using bifurcation and degree theory we then prove the existence of a global continuum of such waves.
In the second part of the thesis we inverstigate an equation which is a model for shallow water waves and waves in a circular cylindrical rod of a compressible hyperelastic material. We present sufficient conditions for global existence and blow-up.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/637730
- author
- Wahlén, Erik LU
- supervisor
- organization
- publishing date
- 2005
- type
- Thesis
- publication status
- published
- subject
- keywords
- water waves, bifurcation, global existence, rod equation, wabve breaking
- pages
- 65 pages
- external identifiers
-
- other:LUNFMA-2014-2005
- other:Licentiate Theses in Mathematical Sciences 2005:8
- language
- English
- LU publication?
- yes
- id
- cdff732b-bc17-481c-9f88-4f811ad8a6f9 (old id 637730)
- date added to LUP
- 2016-04-04 09:09:13
- date last changed
- 2018-11-21 20:51:08
@misc{cdff732b-bc17-481c-9f88-4f811ad8a6f9, abstract = {{In the first part of this thesis we consider the governing equations for capillary water waves given by the Euler equations with a free surface under the influence of surface tension over a flat bottom. We look for two-dimensional steady periodic waves. The problem is first transformed to a nonlinear elliptic equation in a rectangle. Using bifurcation and degree theory we then prove the existence of a global continuum of such waves.<br/><br> <br/><br> In the second part of the thesis we inverstigate an equation which is a model for shallow water waves and waves in a circular cylindrical rod of a compressible hyperelastic material. We present sufficient conditions for global existence and blow-up.}}, author = {{Wahlén, Erik}}, keywords = {{water waves; bifurcation; global existence; rod equation; wabve breaking}}, language = {{eng}}, note = {{Licentiate Thesis}}, title = {{On some Nonlinear Aspects of Wave Motion}}, year = {{2005}}, }