Abels, Helmut and Mora, Maria Giovanna and Mueller, Stefan (2011) Large Time Existence for Thin Vibrating Plates. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 36 (12). pp. 2062-2102. ISSN 0360-5302, 1532-4133
Full text not available from this repository. (Request a copy)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 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | NONLINEAR ELASTICITY; CONVERGENCE; EQUATIONS; SYSTEMS; Dimension reduction; Nonlinear elasticity; Plate theory; Singular perturbation; Von Karman; Wave equation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 29 Jun 2020 09:24 |
| Last Modified: | 29 Jun 2020 09:24 |
| URI: | https://pred.uni-regensburg.de/id/eprint/21542 |
Actions (login required)
 |
View Item |
