Viscoelastic Wave Equation with Variable-Exponent Nonlinear Boundary Feedback

In this paper, we consider a viscoelastic wave equation with a boundary frictional damping having a variable exponent m(x). We investigate the interaction between the two types of dissipative mechanisms and their effects on the energy estimates. Using the multiplier method, we construct explicit formulas, depending on both m and the relaxation function g, which provide faster decay rates than the ones already existing in the literature.