General decay of solutions for a viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary damping-source interactions

A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions imposed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.