相互作用的Brinkman方程组与Darcy方程组解在反应边界条件下的连续依赖性

吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (2): 202-0212.

相互作用的Brinkman方程组与Darcy方程组解在反应边界条件下的连续依赖性

石金诚¹, 夏建业²

1. 广州华商学院数据科学学院, 广州511300； 2. 广东金融学院数学与统计学院, 广州 510521

收稿日期:2021-04-30 出版日期:2022-03-26 发布日期:2022-03-26
通讯作者: 夏建业 E-mail:xiajy1963@163.com

Continuous Dependence of Solutions of Brinkman Equations Interacting with Darcy Equations under Reaction Boundary Conditions

SHI Jincheng¹, XIA Jianye²

1. School of Data Science, Guangzhou Huashang College, Guangzhou 511300, China;
2. School of Mathematics and Statistics, Guangdong University of Finance, Guangzhou 510521, China

Received:2021-04-30 Online:2022-03-26 Published:2022-03-26

摘要/Abstract

摘要： 首先, 利用微分不等式技术得到温度和速度的相关估计, 特别是关于温度的四阶范数估计和速度的梯度估计；其次, 借助先验界构造能量表达式, 推出该表达式所满足的微分不等式；最后, 建立Brinkman-Darcy流体方程组的解对边界系数α的连续依赖性.

关键词: 连续依赖性, Brinkman方程组, Darcy方程组, 边界系数

Abstract: Firstly, the correlation estimates of temperature and velocity were obtained by using differential inequality technique, especially the fourth-order norm estimates of temperature and the gradient estimates of velocity. Secondly, with the help of a priori bound, the energy expression was constructed and the differential inequality satisfied by the expression was derived. Finally, the continuous dependence of solutions of Brinkman-Darcy fluid equations on the boundary coefficients α was established.

Key words: continuous dependence, Brinkman equations, Darcy equations, boundary coefficient

中图分类号:

O175.29

石金诚, 夏建业. 相互作用的Brinkman方程组与Darcy方程组解在反应边界条件下的连续依赖性[J]. 吉林大学学报(理学版), 2022, 60(2): 202-0212.

SHI Jincheng, XIA Jianye. Continuous Dependence of Solutions of Brinkman Equations Interacting with Darcy Equations under Reaction Boundary Conditions[J]. Journal of Jilin University Science Edition, 2022, 60(2): 202-0212.

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