A global nonexistence theorem for viscoelastic equations with arbitrary positive initial energy

AbstractIn this letter we consider the nonlinear viscoelastic equation utt−Δu+∫0tg(t−τ)Δu(τ)dτ+ut=|u|p−1uin Ω×(0,∞) with Dirichlet boundary conditions. Under some appropriate assumptions on g and the initial data, a blow-up result with arbitrary positive initial energy is established for 1<p<nn−2 (if n=1,2, then 1<p<∞)