On Singular Limit and Upper Semicontinuous Family of Attractors of Thermoviscoelastic Berger Plate

Abstract

A system of partial differential equations with integral terms which take into account hereditary effects is considered. The system describes a behaviour of thermoviscoelastic plate with Berger's type of nonlinearity. The hereditary effect is taken into account both in the temperature variable and in the bending one. The main goal of the paper is to analyze the passage to the singular limit when memory kernels collapse into the Dirac mass. In particular, it is proved that the solutions to the system with memory are close in some sense to the solutions to the corresponding memory-free limiting system. Besides, the upper semicontinuity of the family of attractors with respect to the singular limit is obtained.