General decay of solutions for a viscoelastic equation with nonlinear damping and source terms

The initial boundary value problem for a viscoelastic equation |ut|ρ utt − Δu − Δutt + ∫0tg(t − s) Δu(s)ds + |ut|m ut = |u|p uin a bounded domain is considered, where ρ,m,p > 0 and g is a nonnegative and decaying function. The general uniform decay of solution energy is discussed under some conditions on the relaxation function g and the initial data by adopting the method of [14, 15, 19]. This work generalizes and improves earlier results in the literature.