Randomized trial demonstrates finite time blow-up in viscoelastic Kirchhoff-like plate equation solutions, indicating critical thresholds for energy levels.
In this paper, we study the initial-boundary value problem for a viscoelastic Kirchhoff-like plate equation with logarithmic source term. Based on the contraction mapping principle, we prove the local existence and uniqueness of solutions. By the concavity arguments, we obtain the finite time blow-up and estimates on the upper bound for the blow-up time of solutions with negative, null, positive, and arbitrary positive initial energy, respectively.
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Li et al. (2026) studied this question.
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