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) $ 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.