薄膜外延生长的四阶抛物模型解的渐近性质

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

数学季刊 ›› 2022, Vol. 37 ›› Issue (2): 162-177.doi: 10.13371/j.cnki.chin.q.j.m.2022.02.006

薄膜外延生长的四阶抛物模型解的渐近性质

College of Science, China University of Petroleum

收稿日期:2022-03-19 出版日期:2022-06-30 发布日期:2022-06-30
通讯作者: 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. E-mail:fjli@upc.edu.cn
作者简介: 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.
基金资助:
Supported by Shandong Provincial Natural Science Foundation of China (Grant No. ZR2021MA003, ZR2020MA020).

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

College of Science, China University of Petroleum

Received:2022-03-19 Online:2022-06-30 Published:2022-06-30
Contact: 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. E-mail:fjli@upc.edu.cn
About author: 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.
Supported by:
Supported by Shandong Provincial Natural Science Foundation of China (Grant No. ZR2021MA003, ZR2020MA020).

摘要/Abstract

摘要： 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.

关键词: , 4th-Order parabolic equation, Asymptotic estimate, Blow-up, Extinction, Initial energy

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

中图分类号:

O175.26

孙安琪, 李锋杰. 薄膜外延生长的四阶抛物模型解的渐近性质[J]. 数学季刊, 2022, 37(2): 162-177.

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.

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薄膜外延生长的四阶抛物模型解的渐近性质

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

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