中文摘要：

该文研究具有耗散梯度项的一类p-Laplace方程的爆破现象.借助于合适定义的辅助函数和由此产生的一阶微分不等式,分别给出了方程的解爆破与不爆破的条件.另外,当方程的解发生爆破时,还给出了爆破时间的下界估计.

英文摘要：

This paper considers a type of p-Laplace equation with dissipative gradient term.By means of suitable defined auxiliary functions and resulting the first-order differential inequalities,the conditions which ensure that blow-up occurs or does not occur are given.In addition,the lower bound for blow-up time is also determined if blow-up occurs.