This paper investigates the initial boundary value problem for a class of fourth order nonlinear damped wave equations modeling longitudinal motion of an elasto-plastic bar. By applying a suitable potential well-convexity method, we derive the global existence, asymptotic behavior and finite time blow up for the considered problem with more generalized nonlinear functions at subcritical initial energy level. Further for arbitrarily positive initial energy we give some sufficient conditions ensuring finite time blow up.

中文翻译：

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阻尼四阶非线性发展方程的渐近行为和有限时间爆炸

本文研究了一类模拟弹塑性杆纵向运动的四阶非线性阻尼波方程的初始边值问题。通过应用合适的潜在良好的凸性方法，我们得出了在次临界初始能级上具有更广义非线性函数的已考虑问题的整体存在性，渐近行为和有限时间爆炸。此外，对于任意正的初始能量，我们给出一些充分的条件以确保有限的时间爆炸。