Asymptotic Property of Solutions in a 4th-Order Parabolic Model for Epitaxial Growth of Thin Film#br#

SUN An-qi, LI Feng-jie

doi:10.13371/j.cnki.chin.q.j.m.2022.02.006

Chinese Quarterly Journal of Mathematics >

2022 , Vol. 37 >Issue 2: 162 - 177

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.02.006

Asymptotic Property of Solutions in a 4th-Order Parabolic Model for Epitaxial Growth of Thin Film#br#

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College of Science, China University of Petroleum

SUN An-qi (1998-), female, native of Weifang, Shandong, master’s degree candidate of China University of Petroleum, engages in partial differential equation; LI Feng-jie (1974-), female, native of Zhaoyuan, Shandong, associate professor of China University of Petroleum, master supervisor, Ph.D, engages in partial differential equation.

Received date: 2022-03-19

Online published: 2022-06-30

Supported by

Supported by Shandong Provincial Natural Science Foundation of China (Grant No. ZR2021MA003, ZR2020MA020).

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Abstract

This paper deals with a homogeneous Neumann initial-boundary problem of
a 4th-order parabolic equation modeling epitaxial growth of thin film. We determine the
classification of initial energy on the existence of blow-up, global existence and extinction
of solutions by using the potential well method and the auxiliary function method.
Moreover, asymptotic estimates on global solution and extinction solution are studied,
respectively.

Key words： ; 4th-Order parabolic equation; Asymptotic estimate; Blow-up; Extinction; ; Initial energy

Cite this article

SUN An-qi, LI Feng-jie . Asymptotic Property of Solutions in a 4th-Order Parabolic Model for Epitaxial Growth of Thin Film#br#[J]. Chinese Quarterly Journal of Mathematics, 2022 , 37(2) : 162 -177 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.006

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