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Abstract. In this paper, we prove the existence of a global attractor for the suspension bridge equations with nonlinear damping.

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In this paper, we consider a viscoelastic wave equation with variable exponents: utt−Δu+∫0tg(t−s)Δu(s)ds+a|utfalse|m(x)−2ut=b|ufalse|p(x)−2u, 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.

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