Blow-up phenomena for a viscoelastic wave equation with strong damping and logarithmic nonlinearity

In this paper we consider the initial boundary value problem for a viscoelastic wave equation with strong damping and logarithmic nonlinearity of the form utt(x,t)−Δu(x,t)+∫0tg(t−s)Δu(x,s)ds−Δut(x,t)=|u(x,t)|p−2u(x,t)ln|u(x,t)| in a bounded domain Ω⊂ Rⁿ, where g is a nonincreasing positive function. Firstly, we prove the existence and uniqueness of local weak solutions by using Faedo–Galerkin’s method and contraction mapping principle. Then we establish a finite time blow-up result for the solution with positive initial energy as well as nonpositive initial energy.