Uniform rates of decay for full von Kármán systems of dynamic viscoelasticity with memory

Article type: Research Article

Authors: Muñoz Rivera, Jaime E.^; | Perla Menzala, Gustavo^{; ;}

Affiliations: Institute of Mathematics, Federal University of Rio de Janeiro, P.O. Box 68530, Rio de Janeiro, Brazil E‐mail: rivera@lncc.br | National Laboratory for Scientific Computation, Department of Applied and Computational Mathematics, Rua Getulio Vargas 333, Quitandinha 25651‐070, Petrópolis RJ, Brasil E‐mail: perla@lncc.br

Note: [] Corresponding author.

Abstract: In this paper we consider the dynamical full von Kármán system of equations for viscoelastic plates. The main result of this paper says that the uniform rate of decay of the energy function associated with the system depends on the rate of decay of the relaxation functions. Our result can be seem as a refinement of our previous work [23] on the so called “modified” von Kármán model in which case the in‐plane displacements are not taken into account.

Keywords: viscoelasticity, exponential decay, initial boundary value problem

Journal: Asymptotic Analysis, vol. 27, no. 3-4, pp. 335-357, 2001