LAUSR

In this paper, we consider the following nonlinear viscoelastic wave equation with variable exponents: $$u_{tt}-\Delta u+\int_{0}^{t} g(t-\tau)\Delta u(x,\tau)\rm{d}\tau+\mu u_{t}=\vert u\vert^{p(x)-2}u,$$ u t t − Δ u + ∫ 0 t g ( t − τ ) Δ u ( x , τ ) d τ + μ u t = | u | p ( x ) − 2 u , where μ is a nonnegative constant and the exponent of nonlinearity p (·) and g are given functions. Under arbitrary positive initial energy and specific conditions on the relaxation function g , we prove a finite-time blow-up result. We also give some numerical applications to illustrate our theoretical results.