Decay estimate and blow-up for a fourth order parabolic equation modeling epitaxial thin film growth

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 de...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 5; pp. 11297 - 11311
Main Authors Zhang, Hao, Cui, Zejian, Xiao, Xiangyu
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
blow-up
decay estimate
epitaxial thin film growth
parabolic equation
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023572