Thin vibrating plates: long time existence and convergence to the von Kármán plate equations

The asymptotic behavior of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness h of the plate tends to zero. We discuss the long time existence and convergence to solutions of the time-dependent von Kármán and linear plate equation under appropriate scalings of the applied force and of the initial values in terms of h.