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–Pr¨uss–Huang theorem, which characterizes exponential stability, while the polynomial decay rate is obtained using the Borichev and Tomilov theorem.