We consider a reaction–diffusion equation on a 3D thin porous media of thickness \(\varepsilon \) which is perforated by periodically distributed cylinders of size \(\varepsilon \). On the boundary of the cylinders, we prescribe a dynamical boundary condition of pure-reactive type. As \(\varepsilon \rightarrow 0\), in the 2D limit the resulting reaction–diffusion equation has a source term coming from the dynamical-type boundary conditions imposed on boundaries of the original 3D domain.

中文翻译：

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多孔介质上的反应扩散方程

我们考虑一个3D厚度为\（\ varepsilon \）的薄多孔介质的反应扩散方程，该介质由周期分布的大小为\（\ varepsilon \）的圆柱体穿孔。在圆柱的边界上，我们规定了纯反应型的动态边界条件。作为\（\ varepsilon \ rightarrow 0 \），在2D极限中，所得的反应扩散方程的源项来自施加在原始3D域边界上的动态类型边界条件。