论文标题
在不断发展的微型域和包括非线性边界条件的反应扩散 - 介导问题的均质化
Homogenization of a reaction-diffusion-advection problem in an evolving micro-domain and including nonlinear boundary conditions
论文作者
论文摘要
我们考虑在穿孔的培养基中存在反应扩散 - 引入问题，在体积和微观边界中具有非线性反应，并且扩散缩放量低。微观结构在时间上变化；微观结构进化是先验的。本文的目的是均质模型的严格推导。我们使用适当尺度的函数空间，使我们能够显示紧凑的结果，尤其是关于时间衍生的，我们证明了Kolmomogorov-Simon型的强大的两尺度紧凑性结果，这可以在非线性项中传递到极限。派生的宏观模型取决于微观和宏变量，而基础微观结构的演变则由时间和空间依赖性参考元素近似。
We consider a reaction-diffusion-advection problem in a perforated medium, with nonlinear reactions in the bulk and at the microscopic boundary, and low diffusion scaling. The microstructure changes in time; the microstructural evolution is known a priori. The aim of the paper is the rigorous derivation of a homogenized model. We use appropriately scaled function spaces, which allow us to show compactness results, especially regarding the time-derivative and we prove strong two-scale compactness results of Kolmogorov-Simon-type, which allow to pass to the limit in the nonlinear terms. The derived macroscopic model depends on the micro- and the macro-variable, and the evolution of the underlying microstructure is approximated by time- and space-dependent reference elements.
