Global nonexistence of solutions for a nonlinear wave equation with time delay and acoustic boundary conditions

Abstract

We consider a quasilinear wave equation utt−△ut−div(|∇u|α−2∇u)−div(|∇ut|β−2∇ut)+a|ut|m−2ut+μ1ut(x,t)+μ2ut(x,t−τ)=b|u|p−2ua,b>0, associated with initial and Dirichlet boundary conditions at one part and acoustic boundary conditions at another part, respectively. We prove, under suitable conditions on α, β, m, p and for negative initial energy, a global nonexistence of solutions.