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On some Nonlinear Aspects of Wave Motion

In English

Författare

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.

Avdelning/ar

Publiceringsår

2005

Språk

Engelska

Dokumenttyp

Licentiatavhandling

Ämne

  • Mathematics

Nyckelord

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

Status

Published

Forskningsgrupp

  • Partial differential equations

Handledare

  • Adrian Constantin

ISBN/ISSN/Övrigt

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