Large Time Existence for Thin Vibrating Plates

作者：Abels Helmut^*; Mora Maria Giovanna; Mueller Stefan

来源：Communications in Partial Differential Equations, 2011, 36(12): 2062-2102.

DOI：10.1080/03605302.2011.618209

• Dimension reduction
• Nonlinear elasticity
• Plate theory
• Singular perturbation
• Von Karman
• Wave equation

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 Karman 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.

• 出版日期2011