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

Hao Zhang; Zejian Cui; Xiangyu Xiao; Hao Zhang; Zejian Cui; Xiangyu Xiao

doi:10.3934/math.2023572

AIMS Mathematics

2023, Volume 8, Issue 5: 11297-11311. doi: 10.3934/math.2023572

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Research article

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

1.
School of Mathematics and Information, China West Normal University, Nanchong 637002, China
2.
School of Mathematical Sciences, Sichuan Normal University, Chengdu 610068, China

Received: 10 December 2022 Revised: 16 February 2023 Accepted: 27 February 2023 Published: 13 March 2023
MSC : 35B40, 35B44

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.
- parabolic equation,
- epitaxial thin film growth,
- decay estimate,
- blow-up
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

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Abstract

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.

References

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