Calculus of Variations and Geometric Measure Theory

H. Abels - M. G. Mora - S. Müller

The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity

created by mora on 21 Dec 2009
modified on 14 Oct 2011


Published Paper

Inserted: 21 dec 2009
Last Updated: 14 oct 2011

Journal: Calc. Var. Partial Differential Equations
Volume: 41
Pages: 241-259
Year: 2011


The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von Kármán plate equation.

Keywords: dimension reduction, nonlinear elasticity, von Kármán plate equation, wave equation, elastodynamics