Mathematical analysis of a fourth-order degenerate equation with a nonlinear second-order term

IF 0.5 Q4 ENGINEERING, MULTIDISCIPLINARY

Journal of Computational Methods in Sciences and Engineering Pub Date : 2023-06-09 DOI:10.3233/jcm-226854

L. Kong, B. Liang, Y. Li, Y. Wang, Xiaoqin Wu

引用次数: 0

Abstract

A fourth-order partial differential model in this paper is called the thin-film equation in the field of fluid theory. The existence of the weak solution is obtained by solving two approximation problems. In order to perform the limit for small parameters in the approximation problems, the Galerkin method and the entropy functional method are both used. By means of some classical compactness results we can give the existence of nonnegative weak solutions. Finally, by redefining the entropy functional, the long-time exponential decay is given in the sense of L1-norm.

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具有非线性二阶项的四阶退化方程的数学分析

本文提出的四阶偏微分模型在流体理论中称为薄膜方程。通过求解两个近似问题，得到了弱解的存在性。为了在逼近问题中对小参数求极限，采用了伽辽金方法和熵泛函方法。利用一些经典紧性结果，给出了非负弱解的存在性。最后，通过重新定义熵泛函，给出了l1范数意义上的长时间指数衰减。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Methods in Sciences and Engineering ENGINEERING, MULTIDISCIPLINARY-

CiteScore

0.80

自引率

0.00%

发文量

152

期刊介绍： The major goal of the Journal of Computational Methods in Sciences and Engineering (JCMSE) is the publication of new research results on computational methods in sciences and engineering. Common experience had taught us that computational methods originally developed in a given basic science, e.g. physics, can be of paramount importance to other neighboring sciences, e.g. chemistry, as well as to engineering or technology and, in turn, to society as a whole. This undoubtedly beneficial practice of interdisciplinary interactions will be continuously and systematically encouraged by the JCMSE.