On the von Karman Equations - Initial-Boundary Value Problems and Stabilization

Studenteropgave: Kandidatspeciale og HD afgangsprojekt

  • Bjarne Pedersen
  • Henrik Vie Christensen
4. semester, Matematik, Kandidat (Kandidatuddannelse)
The stationary and time-dependent von Karman equations are under consideration in this thesis. In the first part, various preliminary tools are introduced: A product on Sobolev spaces, an existence, uniqueness and regularity theorem for elliptic boundary value problems, some results on the biharmonic operator and the Monge-Amp\''{e}re form, and finaly some theory on dynamical systems and stability. In the second part, the von Karman equations are treated: First it is shown, that a weak solution is continuous with respect to time. Then existence and uniqueness theorems for the time-dependent von Karman equations are shown. Next an existence and a regularity theorem for the stationary von Karman equations are shown. The thesis is concluded with a stabilization result for time-dependent von Karman equations with boundary feedback.
Udgivelsesdatojun. 2002
ID: 61055108