This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a fourth-order parabolic equation with a general nonlinearity. It is shown, under certain conditions on the initial data, that the solutions to this problem blow up in finite time, using differential inequalities. Moreover, upper and lower bounds for the blow-up time are derived when blow-up occurs. This extends and generalizes results obtained by Philippin (Proc AMS. 2015;143(6):2507–13) and by Han (Nonlinear Anal RWA. 2018;43:451–66).

中文翻译：

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具有一般非线性的四阶抛物方程的爆破现象

本文涉及具有一般非线性的四阶抛物方程的初边值问题解的爆破性质。结果表明，在一定条件下的原始数据上，使用微分不等式在有限时间内爆炸了该问题。此外，当发生爆燃时，导出爆燃时间的上限和下限。这扩展并归纳了Philippin（Proc AMS。2015; 143（6）：2507-13）和Han（Nonlinear Anal RWA.2018; 43：451-66）获得的结果。