A class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films

Yang Liu; Wenke Li

doi:10.3934/dcdss.2021112

Article Contents

2021, Volume 14, Issue 12: 4367-4381. Doi: 10.3934/dcdss.2021112 open access

This issue Previous Article Global existence, exponential decay and blow-up of solutions for a class of fractional pseudo-parabolic equations with logarithmic nonlinearity Next Article Inviscid limit for the damped generalized incompressible Navier-Stokes equations on $ \mathbb{T}^2 $

A class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films

Yang Liu^1, and
Wenke Li^2, ,

1.
College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
2.
College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China

^* Corresponding author: liwenke@hrbeu.edu.cn
^* Corresponding author: liwenke@hrbeu.edu.cn

Received: June 30, 2021

Revised: July 31, 2021

Early access: October 2021

Published: December 2021

This work is supported by the Science and Technology Plan Project of Gansu Province in China (Grant No. 21JR1RA200), the Talent Introduction Research Project of Northwest Minzu University (Grant No. xbmuyjrc2021008), the Innovation Team Project of Northwest Minzu University (Grant No. 1110130131), the First-Rate Discipline of Northwest Minzu University (Grant No. 2019XJYLZY-02) and the National Natural Science Foundation of China (Grant No. 12102100)

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Abstract

In this paper, the initial-boundary value problem for a class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films is studied. By means of the theory of potential wells, the global existence, asymptotic behavior and finite time blow-up of weak solutions are obtained.

Keywords:

Fourth-order nonlinear parabolic equations,
existence,
asymptotic behavior,
blow-up.

Mathematics Subject Classification: Primary: 35K35, 35A01, 35B40, 35B44.

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