Asymptotic behavior of a thermoviscoelastic plate with memory effects

TL;DR

This paper analyzes a coupled thermoviscoelastic plate model with memory effects, proving exponential stability and quantifying how the system approximates a memory-free model as memory effects diminish.

Contribution

It establishes exponential stability for a thermoviscoelastic system with hereditary effects and provides estimates on the convergence to a memory-free system.

Findings

System is exponentially stable.

Memory effects diminish as kernels fade, approximating a memory-free system.

Provides quantitative estimates of the convergence.

Abstract

We consider a coupled linear system describing a thermoviscoelastic plate with hereditary effects. The system consists of a hyperbolic integrodifferential equation, governing the temperature, which is linearly coupled with the partial differential equation ruling the evolution of the vertical deflection, presenting a convolution term accounting for memory effects. It is also assumed that the thermal power contains a memory term characterized by a relaxation kernel. We prove that the system is exponentially stable and we obtain a closeness estimate between the system with memory effects and the corresponding memory-free limiting system, as the kernels fade in a suitable sense.