Exponential stability of a viscoelastic plate with thermal memory (Q2726113)

This paper studies the asymptotic behavior of solutions to a model describing the temperature and vertical displacement evolution in a homogeneous, thermally isotropic, Kirchhoff plate composed of a material with linear memory and subject to thermal deformation. In addition, a non-Fourier constitutive law (i.e. the linearized Gurtin-Pipkin heat law) for the heat flux is considered. In spite of the presence of a convolution term, the original problem is transformed into an autonomous system by a suitable choice of variables. As a consequence, the linear semigroup theory is applied and the exponential stability is proved for a class of memory functions including weakly singular kernels which decay exponentially in time. This paper generalizes the known results on the thermoelastic Kirchhoff plate models (without thermal memory) to viscoelastic plates with thermal memory.