This paper is concerned with the study of nonlinear viscoelastic evolution equation with strong damping and source terms, described by utt − Bu + t 0 g(t − τ)Bu(τ )dτ + f (x)ut |ut |m−2 = h(x)|u|p−2u, x ∈ int B, t > 0, where B is a stretched manifold. First, we prove the solutions of problem (1.1) in the cone Sobolev space H1, n 2 2,0 (B), which admit a blow up in finite time for p > m and positive initial energy. Then, we construct a lower bound for obtaining blow up time under appropriate assumptions on data.
