Stabilization for Variable Coefficients Rayleigh Beam Systems under Nonlinear Boundary Controls

This article solves the boundary stabilization problem of variable coefficient Rayleigh beams by using nonlinear boundary feedback controls. The feedback mechanism incorporates a nonlinear function that adheres to a sector condition, thus encompassing a diverse array of nonlinear feedback scenarios. The well-posedness of the closed-loop system is completed by applying nonlinear semigroup theory. The exponential stability of the energy function of a closed-loop system is demonstrated by using the integral multiplier method.