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On some Nonlinear Aspects of Wave Motion

Wahlén, Erik LU (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:
author
supervisor
organization
publishing date
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
2007-12-10 14:10:05
date last changed
2017-02-09 11:55:33
@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},
  keyword      = {water waves,bifurcation,global existence,rod equation,wabve breaking},
  language     = {eng},
  note         = {Licentiate Thesis},
  pages        = {65},
  title        = {On some Nonlinear Aspects of Wave Motion},
  year         = {2005},
}