On the interaction between the viscoelasticity and the boundary variable-exponent nonlinearity in plate systems

In this paper, we consider a viscoelastic plate system with a boundary frictional damping having a variable exponent m(x). We investigate the competition between the two types of damping and their effects on the energy decay rates. Using the multiplier method, we establish explicit decay results depending on both m and the relaxation function g. Our results address both the optimality and generality and improve earlier related results in the literature.