General decay of the solution energy in a viscoelastic equation with a nonlinear source Original Research Article

In a bounded domain, we consider View the MathML sourceutt−Δu+∫0tg(t−τ)Δudτ=|u|γu, Turn MathJax on where View the MathML sourceγ>0and gg is a nonnegative and decaying function. We prove that, for certain class of relaxation functions and certain initial data, the rate of decay of energy is similar to that of gg. This result improves earlier ones in the literature in which only the exponential and polynomial decay rates are considered.