Blow up property for viscoelastic evolution equations on manifolds with conical degeneration

This paper is concerned with the study of nonlinear viscoelastic evolution equation with strong damping and source terms, described by utt-Delta Bu+integral 0tg(t-tau)Delta Bu(tau)d tau+f(x)ut|ut|m-2 =h(x)|u|p-2u,x is an element of intB,t>0, where B is a stretched manifold. First, we prove the solutions of problem (1.1) in the cone Sobolev space H2,01,n2(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.