A general decay result in a quasilinear parabolic system with viscoelastic term

We consider a quasilinear parabolic system of the form A(t)|ut|m−2ut−Δu+∫0tg(t−s)Δu(x,s)ds=0, for m≥2m≥2, A(t)A(t) a bounded and positive definite matrix, and gg a continuously differentiable decaying function and establish a general decay result from which the usual exponential and polynomial decay results are only special cases.