In this paper, we study an anomalous pseudo-parabolic Kirchhoff-type dynamical model aiming to reveal the control problem of the initial data on the dynamical behavior of the solution in dynamic control system. Firstly, the local existence of solution is obtained by employing the Contraction Mapping Principle. Then, we get the global existence of solution, long time behavior of global solution and blowup solution for J ( u 0 ) ⩽ d , respectively. In particular, the lower and upper bound estimates of the blowup time are given for J ( u 0 )< d . Finally, we discuss the blowup of solution in finite time and also estimate an upper bound of the blowup time for high initial energy.

中文翻译：

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异常拟抛物基尔霍夫型动力学模型

在本文中，我们研究了一个异常的伪抛物基尔霍夫型动力学模型，旨在揭示动态控制系统中解的动力学行为的初始数据的控制问题。首先，利用收缩映射原理得到解的局部存在性。然后，我们分别得到 J ( u 0 ) ⩽ d 的全局存在解、全局解的长时间行为和爆破解。特别是，对于 J ( u 0 )< d ，给出了爆破时间的下限和上限估计值。最后，我们讨论了有限时间内解的爆炸，并估计了高初始能量的爆炸时间的上限。