Submitted Paper
(2009)
Authors:
Helmut Abels - Maria Giovanna Mora - Stefan Müller
Pages: 43
Keywords:
wave equation, plate theory, von Kármán theory, nonlinear elasticity, dimension reduction, singular perturbation
Abstract:
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 as h ® 0 is either the nonlinear von Kármán 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.![[PS]](/style/ps.png)
![[PDF]](/style/pdf.png)
[BibTeX Entry]
Available Files:
LongTimeExistence.pdf
abstract.tex (abstract.ps, abstract.pdf)
