论文标题
与连接的多孔培养基的非线性动态Wendzell-interface条件的两相问题的均质化
Homogenization of a two-phase problem with nonlinear dynamic Wentzell-interface condition for connected-disconnected porous media
论文作者
论文摘要
我们研究了在不同成分之间具有非线性界面条件的两个组分多孔培养基中的反应扩散问题。一个组件已连接，另一个组件断开了连接。小参数$ε$描述了微观孔尺度和整个域的大小之间的比率。在组件之间的界面上，我们考虑了动态的温泽尔 - 结合条件，其中来自散装域的正常通量是由反应扩散方程式给出的散装痕迹的反应扩散方程，包括非线性反应 - 金属溶液，具体取决于界面两侧的溶液。使用两尺度的技术，我们将$ε\ \至0 $传递，并得出宏观模型，在该模型中我们需要表面扩散的均匀化结果。为了应对非线性术语，我们得出了强大的两尺度结果。
We investigate a reaction-diffusion problem in a two-component porous medium with a nonlinear interface condition between the different components. One component is connected and the other one is disconnected. The ratio between the microscopic pore scale and the size of the whole domain is described by the small parameter $ε$. On the interface between the components we consider a dynamic Wentzell-boundary condition, where the normal fluxes from the bulk-domains are given by a reaction-diffusion equation for the traces of the bulk-solutions, including nonlinear reaction-kinetics depending on the solutions on both sides of the interface. Using two-scale techniques, we pass to the limit $ε\to 0$ and derive macroscopic models, where we need homogenization results for surface diffusion. To cope with the nonlinear terms we derive strong two-scale results.
