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

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.

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

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.