TY - JOUR
T1 - Large Time Existence for Thin Vibrating Plates
JF - Communication in Partial Differential Equations 36 (2011) 2062-2102
Y1 - 2011
A1 - Helmut Abels
A1 - Maria Giovanna Mora
A1 - Stefan Müller
AB - 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.
PB - Taylor & Francis
UR - http://hdl.handle.net/1963/3755
U1 - 562
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity
JF - Calculus of Variations and Partial Differential Equations 41 (2011) 241-259
Y1 - 2011
A1 - Helmut Abels
A1 - Maria Giovanna Mora
A1 - Stefan Müller
AB - 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.
PB - Springer
UR - http://hdl.handle.net/1963/3835
U1 - 492
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -