关键词: 四阶抛物方程, 微分不等式, 爆破时刻的上界, 爆破时刻的下界

Abstract: We considered the blow-up phenomena of solutions to  a class of fourth-order parabolic equations. Firstly, we  introduced a new inequality. Secondly, under appropriate conditions, we  proved that the solution to the equation blew up in finite time and gave an upper bound estimate for the blow-up time. Finally, using the new inequality and differential inequality techniques, we obtained a lower bound estimate for the blow-up time of the solution.

Key words: fourth-order parabolic equation, differential inequality, upper bound for , blow-up time, lower bound for , blow-up time