Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay - Lin Rongrui; Gao Yunlong; She Lianbing (Open Mathematics)
We study the Euler-Bernoulli equations with time delay: utt+Δ2u−g1∗Δ2u+g2∗Δu+μ1ut(x,t)∣ut(x,t)∣m−2+μ2ut(x,t−τ)∣ut(x,t−τ)∣m−2=f(u),{u}_{tt}+{Δ }^{2}u-{g}_{1}* {Δ }^{2}u+{g}_{2}* Δ u+{μ }_{1}{u}_{t}\left(x,t){| {u}_{t}\left(x,t)| }^{m-2}+{μ }_{2}{u}_{t}\left(x,t-τ ){| {u}_{t}\left(x,t-τ )| }^{m-2}=f\left(u), where ττ 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.