In this paper, we study a fourth order parabolic equation modeling epitaxial thin film growth. By using the potential well method and some inequality techniques, we obtain the decay estimate of weak solutions. Meanwhile, the blow-up time is estimated from above and below. The blow-up rate is also derived.
Citation: Hao Zhang, Zejian Cui, Xiangyu Xiao. Decay estimate and blow-up for a fourth order parabolic equation modeling epitaxial thin film growth[J]. AIMS Mathematics, 2023, 8(5): 11297-11311. doi: 10.3934/math.2023572
In this paper, we study a fourth order parabolic equation modeling epitaxial thin film growth. By using the potential well method and some inequality techniques, we obtain the decay estimate of weak solutions. Meanwhile, the blow-up time is estimated from above and below. The blow-up rate is also derived.
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