Nonlinear damping effects for the 2D Mindlin–Timoshenko system

Abstract In this article, we investigate the asymptotic behavior of the Mindlin–Timoshenko system under the influence of nonlinear dissipation affecting the rotation angle equations. Initially, we provide a concise review of the system’s solution existence. Subsequently, we demonstrate that the energy associated with the solution of the Mindlin–Timoshenko setup follows a dissipation. Furthermore, under the condition of equal wave speeds, we establish a comprehensive decay theorem for the energy, offering explicit insights into its general behavior.