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Research Article | Open Access

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

Hao Zhang1, Zejian Cui1( ), Xiangyu Xiao2
School of Mathematics and Information, China West Normal University, Nanchong 637002, China
School of Mathematical Sciences, Sichuan Normal University, Chengdu 610068, China
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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.

Keywords

parabolic equationepitaxial thin film growthdecay estimateblow-up
CLC number: 35B40, 35B44

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AIMS Mathematics
Volume 8 Issue 5,
May 2023
Pages 11297-11311
DOI: 10.3934/math.2023572

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Cite this article:
Zhang H, Cui Z, Xiao X. Decay estimate and blow-up for a fourth order parabolic equation modeling epitaxial thin film growth. AIMS Mathematics, 2023, 8(5): 11297-11311. https://doi.org/10.3934/math.2023572

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Received: 10 December 2022
Revised: 16 February 2023
Accepted: 27 February 2023
Published: 15 May 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)