Blow-up results for viscoelastic wave equations with weak damping. (June 2018) - Park, Sun-Hye; Lee, Mi Jin; Kang, Jum-Ran
Abstract: In this work we consider a viscoelastic wave equation of the form u t t − Δ u + ∫ 0 t g ( t − s ) Δ u ( s ) d s + h ( u t ) = | u | p − 2 u with Dirichlet boundary condition. There are much literature on the blow-up result of solutions for the wave equation with damping term having polynomial growth near zero. However, to my knowledge, there is no blow-up result of solutions for the viscoelastic wave equation without polynomial growth near zero assumption on the damping term. This work is devoted to study a finite time blow-up result of solution with nonpositive initial energy as well as positive initial energy without imposing any restrictive growth near zero assumption on the damping term.