Blow-up Solutions to Logarithmic Viscoelastic Equations with Nonlocal Weak Damping, Delay, and Acoustic Boundary Conditions
DOI:
https://doi.org/10.61383/ejam.202532102Keywords:
Finite time blow-up, Logarithmic viscoelastic equations, Nonlocal weak damping term, Time delay, Acoustic boundary conditionsAbstract
We in this paper consider the blow-up behavior of any nontrivial solution to the following initial boundary value problem of the logarithmic viscoelastic equations with delay and nonlocal weak damping terms under acoustic boundary conditions \[\begin{aligned} u_{tt} - \Delta u + \|u_t\|^k_2u_t &+ \int^t_0\omega(t-s)\Delta u(s)ds +c_1|u_t(t)|^{m-2}u_t(t)\\ & +c_2|u_t(t-\tau)|^{m-2}u_t(t-\tau) =|u|^{p-2}u\ln |u|. \end{aligned} \] Our results show that the local solution blows up in finite time if $p > m$ and $E(0) < 0$. More accurately, we give the upper bound of the blow-up time by the energy method. Moreover, we also give the lower bound of the blow-up time.References
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