一类含有Soret项的Brinkman方程组的结构稳定性
Structural Stability of a Class of Brinkman Equations with Soret Term
DOI: 10.12677/PM.2022.1211218, PDF,    科研立项经费支持
作者: 程健燊：广东金融学院应用数学系，广东 广州
关键词: Brinkman方程组；连续依赖性；Brinkman系数；Soret系数；Brinkman Equations； Continuous Dependence； Brinkman Coefficient； Soret Coefficient
摘要: 考虑了具有Soret效应的Brinkman方程组的解对方程系数 的连续依赖性。首先，运用微分不等式技术，得到温度和盐浓度的相关估计，尤其是获得了盐浓度的四阶范数估计；其次，利用先验估计，推导出能量函数所满足的微分不等式；最后，求解该不等式，建立了解对系数 的连续依赖性结果，该结果表明系数 的微小变化不会引起解的急剧变化，因此Brinkman方程组对Soret系数具有结构稳定性。
Abstract: The continuous dependence of the solution of Brinkman equations with Soret effect on equation coefficient is considered. Firstly, the correlation estimates of temperature and salt concentra-tion are obtained by using differential inequality technique. Especially, we can get the fourth-order norm estimates for the concentration of the salt. Secondly, the differential inequality satisfied by the energy function is derived by using a priori estimate. Finally, by solving the inequality, the continuous dependence of solution on coefficient is established, the results show that the small change of coefficient will not cause the sharp change of solution, so Brinkman equations have structural stability for Soret coefficients.
文章引用：程健燊. 一类含有Soret项的Brinkman方程组的结构稳定性[J]. 理论数学, 2022, 12(11): 2011-2020. https://doi.org/10.12677/PM.2022.1211218

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