论文标题
瓶颈里
Canards in a bottleneck
论文作者
论文摘要
在本文中，我们研究了具有小扩散和非线性内部和流出边界条件的非线性fokker-Planck方程的固定曲线。我们认为带有瓶颈的走廊，其宽度在内部具有最小的全球非排定。在小型扩散极限中，使用从几何奇异扰动理论（GSPT）的方法建设性地获得了曲线。我们确定了与：（i）域中的高密度和入口处的边界层相对应的三种主要轮廓类型，（ii）域中的低密度和出口处的边界层，以及（iii）从高密度到瓶颈内部的高密度到瓶颈内部层，并在入口处和出口处进行边界层。有趣的是，最后类型的解决方案涉及在瓶颈最狭窄点产生的牛排溶液。我们从内和流出率方面获得了这些解决方案的详细分叉图。通过研究带有可变宽度瓶颈的走廊的计算实验，基于GSPT的分析结果得到了进一步的证实。
In this paper we investigate the stationary profiles of a nonlinear Fokker-Planck equation with small diffusion and nonlinear in- and outflow boundary conditions. We consider corridors with a bottleneck whose width has a global nondegenerate minimum in the interior. In the small diffusion limit the profiles are obtained constructively by using methods from geometric singular perturbation theory (GSPT). We identify three main types of profiles corresponding to: (i) high density in the domain and a boundary layer at the entrance, (ii) low density in the domain and a boundary layer at the exit, and (iii) transitions from high density to low density inside the bottleneck with boundary layers at the entrance and exit. Interestingly, solutions of the last type involve canard solutions generated at the narrowest point of the bottleneck. We obtain a detailed bifurcation diagram of these solutions in terms of the in- and outflow rates. The analytic results based on GSPT are further corroborated by computational experiments investigating corridors with bottlenecks of variable width.
