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

The initial boundary value problem for a viscoelastic equation |ut|ρutt−Δu−Δutt+∫0tg(t−s)Δu(s)ds+|ut|mut=|u|pu in 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.

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