BLOW UP OF SOLUTIONS FOR VISCOELASTIC WAVE EQUATIONS OF KIRCHHOFF TYPE WITH ARBITRARY POSITIVE INITIAL ENERGY

In this article we consider the nonlinear Viscoelastic wave equations of Kirchh off type u(tt) - M(parallel to del u parallel to(2))Delta u + integral(t)(0) g(1)(t - tau)Delta u(tau)d tau + u(t) = (p + 1)vertical bar v vertical bar(q+1)vertical bar u vertical bar(p-1) u, u(tt) - M(parallel to del v parallel to(2))Delta v + integral(t)(0) g(2)(t - tau)Delta v(tau)d tau + v(t) = (q + 1)vertical bar u vertical bar(p+1)vertical bar v vertical bar(q-1) v, with initial conditions and Dirichlet boundary conditions. We proved the global nonexistence of solutions by applying a lemma by Levine, and the concavity method.