Decay rates for the energy of a singular nonlocal viscoelastic system

Abstract

This work deals with decay rates for the energy of an initial boundary value problem with a nonlocal boundary condition for a system of nonlinear singular viscoelastic equations. We prove the decay rates for the energy of a singular one‐dimensional viscoelastic system with a nonlinear source term and nonlocal boundary condition of relaxation kernels described by the inequality for all t ≥ 0, with H convex.