Blow up in a nonlinear viscoelastic wave equation with strong damping

• DOI: 10.1016/j.na.2014.06.012
• Publication Date: 2014-07-31T05:46:43Z
• Authors: Haitao Song; Desheng Xue
• Keywords: 0101 mathematics; 01 natural sciences

Abstract In this paper, we consider the nonlinear viscoelastic equation: u t t − △ u + ∫ 0 t g ( t − τ ) △ u ( τ ) d τ − △ u t = ∣ u ∣ p − 2 u , in Ω × [ 0 , T ] , with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g , we show the finite time blow up of some solutions whose initial data have arbitrarily high initial energy.