标题： 一种一维流动的PDE模型：定态解和渐近行为 显示英文标题

标题： A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour

摘要： 在本文中，我们研究了具有单个入口和出口的区域中单向行人流的对流-扩散模型的稳态轮廓。 入口和出口处的流入和流出条件以及区域的形状对稳态轮廓的结构，特别是边界层的形成有显著影响。 我们能够通过几何奇异摄动理论将这些层的位置和形状与流入和流出条件以及区域的形状联系起来。 此外，我们通过计算实验确认并举例说明了我们的分析结果。 显示英文摘要

摘要： 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.