On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth
type: Item
instance of: scholarly article
title: On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth
zbMATH Open document ID: 1389.35188
author: Ning Duan
author: Xiaopeng Zhao
author: Xiufang Zhao
published in: Mathematica Slovaca
publication date: 2016-10-14T00:00:00Z
Mathematics Subject Classification ID: 35K35
zbMATH DE Number: 6639557
zbMATH Keywords: fourth order parabolic equation
zbMATH Keywords: existence
zbMATH Keywords: regularity
zbMATH Keywords: global attractor
MaRDI profile type: Publication
full work available at URL: ms-2015-0167
OpenAlex ID: W2511666498
DOI: 10.1515/MS-2015-0167
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review text: The authors consider the fourth order parabolic equation modeling epitaxial thin film growth NEWLINE\[NEWLINE \frac {\partial u}{\partial t}=-\nabla \cdot \Bigl [m(x,t)\bigl (k\nabla \Delta u-| \nabla u| ^{p-2}\nabla u\bigr)\Bigr],\qquad k>0,\quad p>2. NEWLINE\]NEWLINE They proved the existence and uniqueness of global weak solution for the initial and boundary problem in the space \(H^{4,1}(Q_T)\). Based on the framework of Campanato spaces, authors established the regularity of the solutions in two space dimensions. Using Temam's classical theorem, they proved that the problem admitted a global attractor in the space \(H^2(\Omega)\).
description: scientific article; zbMATH DE number 6639557