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On some Nonlinear Aspects of Wave Motion

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Author

Summary, in English

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.

Department/s

Publishing year

2005

Language

English

Document type

Licentiate thesis

Topic

  • Mathematics

Keywords

  • water waves
  • bifurcation
  • global existence
  • rod equation
  • wabve breaking

Status

Published

Research group

  • Partial differential equations

Supervisor

  • Adrian Constantin

ISBN/ISSN/Other

  • LUNFMA-2014-2005
  • Licentiate Theses in Mathematical Sciences 2005:8