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

Abstract

In this paper we consider the viscoelastic wave equation of Kirchhoff type: $$u_{tt}-M(\Vert \nabla u{\Vert }_2^2)\Delta u+{\int }_0^{t}g(t-s)\Delta u(s)\mathrm{d}s+u_t=|u{|}^{p-1}u$$ 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.

12 pages