%0 Journal Article
%J Communication in Partial Differential Equations 36 (2011) 2062-2102
%D 2011
%T Large Time Existence for Thin Vibrating Plates
%A Helmut Abels
%A Maria Giovanna Mora
%A Stefan Müller
%X 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.
%B Communication in Partial Differential Equations 36 (2011) 2062-2102
%I Taylor & Francis
%G en_US
%U http://hdl.handle.net/1963/3755
%1 562
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-15T09:12:35Z\\r\\nNo. of bitstreams: 1\\r\\nLongTimeExistence.pdf: 331066 bytes, checksum: eba3dcbc86ddcd7b92e10fddca5964c4 (MD5)
%R 10.1080/03605302.2011.618209
%0 Journal Article
%J Calculus of Variations and Partial Differential Equations 41 (2011) 241-259
%D 2011
%T The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity
%A Helmut Abels
%A Maria Giovanna Mora
%A Stefan Müller
%X The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation.
%B Calculus of Variations and Partial Differential Equations 41 (2011) 241-259
%I Springer
%G en_US
%U http://hdl.handle.net/1963/3835
%1 492
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-26T16:49:12Z\\r\\nNo. of bitstreams: 1\\r\\n0912.4135v1.pdf: 217528 bytes, checksum: 4ee557860670b3d876174b2e053958e4 (MD5)
%R 10.1007/s00526-010-0360-0