论文标题
单向流的PDE模型：固定轮廓和渐近行为
A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour
论文作者
论文摘要
在本文中，我们研究了一个单个入口和出口的域中单向行人流的对流扩散模型的固定曲线。入口和出口的流入和流出条件以及域的形状都对固定轮廓的结构有很大影响，特别是对边界层的形成。我们能够使用几何奇异扰动理论将这些层的位置和形状与流入和流出条件以及域的形状联系起来。此外，我们通过计算实验来确认和体现我们的分析结果。
In this paper, we investigate the stationary profiles of a convection-diffusion model for unidirectional pedestrian flows in domains with a single entrance and exit. The inflow and outflow conditions at both the entrance and exit as well as the shape of the domain have a strong influence on the structure of stationary profiles, in particular on the formation of boundary layers. We are able to relate the location and shape of these layers to the inflow and outflow conditions as well as the shape of the domain using geometric singular perturbation theory. Furthermore, we confirm and exemplify our analytical results by means of computational experiments.
