On the internal and boundary stabilization of a nonlinear suspension bridge system: exponential and polynomial decay rates

In this paper, we study the asymptotic behavior of solutions for unconstrained one dimensional suspension bridge model. We dissipate the system with two nonlinear dampings of variable exponents-type. We obtain exponential and polynomial decay results based on the range of the variable exponents by using the multiplier method. Our results built on, developed and generalized some earlier results in the literature.