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

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