Blow up of arbitrarily positive initial energy solutions for a viscoelastic wave equation. (December 2015) - Song, Haitao
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 | m − 2 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.