Abstract We consider the initial boundary value problem of pseudo-parabolic equation with singular potential. We obtain global existence, asymptotic behavior and blowup of solutions with initial energy J ( u 0 ) ≤ d . Moreover, we estimate the upper bound of the blowup time for J ( u 0 ) 0 and 0 J ( u 0 ) d respectively. Finally, we prove the finite time blowup and estimate the upper bound of the blowup time for the high energy level, i.e., J ( u 0 ) > 0 .

中文翻译：

---

具有奇异势的拟抛物方程解的全局存在性和爆破

摘要 考虑具有奇异势的拟抛物线方程的初边值问题。我们获得初始能量 J ( u 0 ) ≤ d 的解的全局存在性、渐近行为和爆炸。此外，我们分别估计了 J (u 0 ) 0 和 0 J ( u 0 ) d 的爆破时间的上限。最后，我们证明了有限时间膨胀，并估计了高能级的膨胀时间上限，即 J ( u 0 ) > 0 。