论文标题
在临界扩散率的情况下，通过一系列薄通道的反应扩散传输的奇异极限
Singular limit for reactive diffusive transport through an array of thin channels in case of critical diffusivity
论文作者
论文摘要
我们考虑了一个非线性反应 - 扩散方程，该域中由两个大型区域组成，这些区域是通过定期分布在薄层内的小通道连接的。通道的高度和厚度为$ε$，并且该层内的方程取决于参数$ε$。我们考虑在通道中的扩散系数和通道横向边界上的非线性诺伊曼 - 边界条件的临界缩放。当通道障碍被两个散装域之间的接口$σ$取代时，我们在限制$ε\至0 $中得出有效的模型。由于扩散系数的临界大小，我们在$σ$上获得了解决方案及其正常通量的跳跃，涉及接口$σ$的每个点上参考通道上本地单元格问题的解决方案。
We consider a nonlinear reaction--diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order $ε$, and the equation inside the layer depends on the parameter $ε$. We consider the critical scaling of the diffusion coefficients in the channels and nonlinear Neumann-boundary condition on the channels' lateral boundaries. We derive effective models in the limit $ε\to 0 $, when the channel-domain is replaced by an interface $Σ$ between the two bulk-domains. Due to the critical size of the diffusion coefficients, we obtain jumps for the solution and its normal fluxes across $Σ$, involving the solutions of local cell problems on the reference channel in every point of the interface $Σ$.
