This paper deals with a fourth-order parabolic equation with/without p-Laplician and general nonlinearity modeling epitaxial growth. By using the variational structure of the problem and differential inequalities, it is shown, under some conditions on the initial value, the solutions to the problem will blow up in finite time. Furthermore, the upper bound of the blow-up time for blowing-up solution is given. Moreover, the existence of a ground-state solution is obtained under approximate assumptions on the nonlinear term. The results of this paper extend and generalize some results got in the papers [G. A. Philippin, Blow-up phenomena for a class of fourth-order parabolic problems, Proceedings of the American Mathematical Society, 143(6): 2507–2513, 2015], [Y. Z. Han, A class of fourth-order parabolic equation with arbitrary initial energy, Nonlinear Anal. Real World Appl., 43: 451–466, 2018], and [J. Zhou, Global asymptotical behavior of solutions to a class of fourth order parabolic equation modeling epitaxial growth, Nonlinear Anal. Real World Appl., 48: 54–70, 2019].

这篇论文讨论了一个有/没有p的四阶抛物线方程-Laplician 和一般非线性建模外延生长。利用问题的变分结构和微分不等式表明，在初始值的某些条件下，问题的解将在有限时间内爆炸。此外，还给出了吹气溶液的吹气时间上限。此外，基态解的存在是在非线性项的近似假设下获得的。本文的结果扩展和概括了论文 [GA Philippin，一类四阶抛物线问题的爆炸现象，美国数学会会刊，143(6): 2507–2513, 2015] 中的一些结果, [YZ Han, 一类具有任意初能的四阶抛物线方程, 非线性分析. Real World Appl., 43: 451–466, 2018] 和 [J. 周，一类模拟外延生长的四阶抛物线方程解的全局渐近行为，非线性分析。真实世界应用，48：54–70，2019 年]。