You are here

Large Time Existence for Thin Vibrating Plates

TitleLarge Time Existence for Thin Vibrating Plates
Publication TypeJournal Article
Year of Publication2011
AuthorsAbels, H, Mora, MG, Müller, S
JournalCommunication in Partial Differential Equations 36 (2011) 2062-2102

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\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.


Sign in