In this work, we investigate blowup phenomena for nonlinearly damped viscoelastic equations with logarithmic source effect and time delay in the velocity. Owing to the nonlinear damping term instead of strong or linear dissipation, we cannot apply the concavity method introduced by Levine. Thus, utilizing the energy method, we show that the solutions with not only non-positive initial energy but also some positive initial energy blow up at a finite point in time.

中文翻译：

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具有对数源和延迟项的非线性阻尼粘弹性方程的 Blowup

在这项工作中，我们研究了具有对数源效应和速度时间延迟的非线性阻尼粘弹性方程的膨胀现象。由于非线性阻尼项而不是强或线性耗散，我们不能应用 Levine 引入的凹度方法。因此，利用能量方法，我们证明了不仅具有非正初始能量而且具有一些正初始能量的解在有限的时间点爆炸。