  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 K\'arm\'an plate equation.

Analysis of PDEs