A Kirchhoff-type parabolic equation with logarithmic nonlinearity is studied in this paper. By employing the potential well theory and some differential inequality techniques, a new blow-up condition, the upper bound of the blow-up time, and the lower bound of the growth rate of blow-up solutions are obtained. The effect of the parameters $a,b,\theta$ in the assumption of Kirchhoff function $M$ is simultaneously considered, while Ding and Zhou only considered the effect of the parameters $b,\theta$. Thus, the main result in the present paper improves a recent blow-up result.

中文翻译：

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具有对数非线性的Kirchhoff型抛物方程的爆破现象

研究了具有对数非线性的Kirchhoff型抛物方程。通过利用势阱理论和一些微分不等式技术，获得了新的爆炸条件，爆炸时间的上限和爆炸溶液的增长率的下限。参数的效果$\mathrm{一种}，b，\theta$ 在基尔霍夫函数的假设下 $\mathrm{中号}$ 同时考虑，而丁和周只考虑了参数的影响 $b，\theta$。因此，本文的主要结果改善了最近的爆破结果。