Large time existence for thin vibrating plates

We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system is either the nonlinear von Kármán plate equation or the linear plate equation. In the latter case we also obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.