Analysis and Optimal Control of a System of Hemivariational Inequalities Arising in Non-Stationary Navier-Stokes Equation with Thermal Effects

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-01 DOI:10.4208/nmtma.oa-2023-0124

Hailing Xuan,Xiaoliang Cheng, Xilu Wang

引用次数: 0

Abstract

In this paper, we primarily investigate the existence, dependence and optimal control results related to solutions for a system of hemivariational inequalities pertaining to a non-stationary Navier-Stokes equation coupled with an evolution equation of temperature field. The boundary conditions for both the velocity field and temperature field incorporate the generalized Clarke gradient. The existence and uniqueness of the weak solution are established by utilizing the Banach fixed point theorem in conjunction with certain results pertaining to hemivariational inequalities. The finite element method is used to discretize the system of hemivariational inequalities and error bounds are derived. Ultimately, a result confirming the existence of a solution to an optimal control problem for the system of hemivariational inequalities is elucidated.

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带有热效应的非静态纳维-斯托克斯方程中出现的半变量不等式系统的分析与优化控制

本文主要研究了与非稳态纳维-斯托克斯方程和温度场演化方程耦合的半变量不等式系统解的存在性、依存性和最优控制结果。速度场和温度场的边界条件都包含广义克拉克梯度。弱解的存在性和唯一性是通过利用巴拿赫定点定理和有关半变量不等式的某些结果来确定的。利用有限元方法对半变量不等式系统进行离散化，并推导出误差边界。最后，阐明了确认半变量不等式系统最优控制问题解存在的结果。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.