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

IF 1.9 4区数学 Q1 MATHEMATICS

Numerical Mathematics-Theory Methods and Applications Pub Date : 2024-05-01 DOI:10.4208/nmtma.oa-2023-0124

Hailing Xuan,Xiaoliang Cheng, Xilu Wang

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引用次数: 0

摘要

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

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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来源期刊

Numerical Mathematics-Theory Methods and Applications 数学-数学

CiteScore

2.80

自引率

7.70%

发文量

审稿时长

>12 weeks

期刊介绍： Numerical Mathematics: Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction, analysis and application of numerical methods for solving scientific and engineering problems. Important research and expository papers devoted to the numerical solution of mathematical equations arising in all areas of science and technology are expected. The journal originates from the journal Numerical Mathematics: A Journal of Chinese Universities (English Edition). NM-TMA is a refereed international journal sponsored by Nanjing University and the Ministry of Education of China. As an international journal, NM-TMA is published in a timely fashion in printed and electronic forms.