Stabilization of a Rao-Nakra Sandwich Beam System by Coleman-Gurtin's Thermal Law and Nonlinear Damping of Variable-Exponent Type

In this paper, we explore the asymptotic behavior of solutions in a thermoplastic Rao-Nakra (sandwich beam) beam equation featuring nonlinear damping with a variable exponent. The heat conduction in this context adheres to Coleman-Gurtin's thermal law, encompassing linear damping, Fourier, and Gurtin-Pipkin's laws as specific instances. By employing the multiplier approach, we establish general energy decay results, with exponential decay as a particular manifestation. These findings extend and generalize previous decay results concerning the Rao-Nakra sandwich beam equations.