On the viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources with variable-exponent nonlinearities

Abstract

This work is devoted to the study of a nonlinear viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping and nonlinear boundary interior sources with variable exponents. Under appropriate assumptions, we establish a 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.