# Large Time Existence for Thin Vibrating Plates

created by mora on 14 Sep 2009
modified on 09 Jul 2012

[BibTeX]

Published Paper

Inserted: 14 sep 2009
Last Updated: 9 jul 2012

Journal: Comm. Partial Differential Equations
Volume: 36
Pages: 2062-2102
Year: 2011

Abstract:

We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as $h \to 0$ is either the nonlinear von Kármán plate equation or the linear fourth order Germain-Lagrange equation. In the case of the linear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.