Global nonexistence of solutions for the viscoelastic wave equation of Kirchhoff type with high energy

In this paper we consider the viscoelastic wave equation of Kirchhoff type: $$u_{tt}-M(\mathrm{\parallel }\mathrm{\nabla }u{\mathrm{\parallel }}_2^2)\mathrm{\Delta }u+{\int }_0^{t}g(t-s)\mathrm{\Delta }u(s)\mathrm{d}s+u_t=\mathrm{\mid }u{\mathrm{\mid }}^{p-1}u$$ with Dirichlet boundary conditions. Under some suitable assumptions on $g$ and the initial data, we established a global nonexistence result for certain solutions with arbitrarily high energy.