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: $u_{tt}-M(\|\nabla u\|_{2}^{2})Δu+\int_{0}^{t}g(t-s)Δu(s){\rm d}s+u_{t}=|u|^{p-1}u$ 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.

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