On the von Karman Equations - Initial-Boundary Value Problems and Stabilization
Translated title
Authors
Term
4. term
Education
Publication year
2002
Submitted on
2012-02-14
Abstract
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.
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