Stability results for a laminated thermoviscoelastic system with Fourier’s law

Abstract

In this paper, we study the qualitative behavior of a mathematical model for two-layered beams with Kelvin–Voigt damping acting at the shear angle. The model describes the behavior of two-layered beams in which slip can occur at the interface with thermodiffusion effects under Fourier’s law. We use semigroups of linear operators theory to prove the proposed problem’s well-posedness and exponential and polynomial stability results in each case addressed. Our stability approach is based on the Gearhart–Prüss–Huang theorem, which characterizes exponential stability, while the polynomial decay rate is obtained using the Borichev and Tomilov theorem.