Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay

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Abstract We study the Euler-Bernoulli equations with time delay: u t t + Δ 2 u − g 1 ∗ Δ 2 u + g 2 ∗ Δ u + μ 1 u t ( x , t ) ∣ u t ( x , t ) ∣ m − 2 + μ 2 u t ( x , t − τ ) ∣ u t ( x , t − τ ) ∣ m − 2 = f ( u ) , {u}_{tt}+{\Delta }^{2}u-{g}_{1}\ast {\Delta }^{2}u+{g}_{2}\ast \Delta u+{\mu }_{1}{u}_{t}\left(x,t){| {u}_{t}\left(x,t)| }^{m-2}+{\mu }_{2}{u}_{t}\left(x,t-\tau ){| {u}_{t}\left(x,t-\tau )| }^{m-2}=f\left(u), where τ \tau represents the time delay. We exhibit the blow-up behavior of solutions with both positive and nonpositive initial energy for the Euler-Bernoulli equations involving time delay.