Blow‐up of solutions for a viscoelastic wave equation with variable exponents

In this paper, we consider a viscoelastic wave equation with variable exponents:u t t − Δ u + ∫ 0 t g ( t − s ) Δ u ( s ) d s + a | u t | m ( x ) − 2u t = b | u | p ( x ) − 2 u , where the exponents of nonlinearity p (·) and m (·) are given functions and a , b  > 0 are constants. For nonincreasing positive function g , we prove the blow‐up result for the solutions with positive initial energy as well as nonpositive initial energy. We extend the previous blow‐up results to a viscoelastic wave equation with variable exponents.