薄膜外延生长的四阶抛物模型解的渐近性质

孙安琪, 李锋杰

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

数学季刊 >

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

DOI: https://doi.org/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

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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.

收稿日期: 2022-03-19

网络出版日期: 2022-06-30

基金资助

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

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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

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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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

本文引用格式

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

Abstract

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

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