Global and blow‐up of solutions for a quasilinear parabolic system with viscoelastic and source terms

In this work, we consider an initial boundary value problem related to the quasilinear parabolic equation A ( t ) | u t| m − 2u t − △ u + ∫ 0 t g ( t − s ) △ u ( x , s ) d s = | u | p − 2 u , for m  ≥ 2, p  ≥ 2, A ( t ) a bounded and positive definite matrix, and g a continuously differentiable decaying function, and prove, under suitable conditions on g and p , a general decay of the energy function for the global solution and a blow‐up result for the solution with both positive and negative initial energy. Copyright © 2013 John Wiley & Sons, Ltd.