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

Abstract

In this paper, we consider a viscoelastic wave equation with variable exponents: urn:x-wiley:mma:media:mma5501:mma5501-math-0001 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.