关键词: 奇异项, 对数非线性项, 四阶, 整体存在, 爆破

Abstract: We considered a class of fourth-order thin-film equation with singular term and logarithmic source. Firstly, we obtained the local existence of weak solutions to the equation by  combining truncation function and  Galerkin approximation. Secondly, by virtue of the potential well method and Rellich inequality, we proved the global existence and decay estimate of weak solution to the equation under certain conditions. Finally, we proved the blow-up result of the  solution to the equation at a finite time by using the convex method, and gave the lower and upper bounds for blow-up time.

Key words: singular term, logarithmic nonlinearity, fourth-order, global existence, blow-up