负扩散率集体运动模型中的粘性剖面
Viscous profiles in models of collective movements with negative diffusivities
摘要：
本文考虑一维空间中扩散系数可以为负的对流-扩散方程。这样的方程特别出现在车辆交通流或人群动力学的建模中，其中负扩散率模拟聚集现象。我们专注于行波解决方案，连接两个国家的扩散具有不同的迹象，在一些几何条件下，我们证明了存在性，唯一性（在一个合适的类解决方案，避免高原）和锋利的相应配置文件。这样的结果，然后扩展到的情况下，扩散率是积极的，但它成为负的，在它们之间的一些间隔的结束状态。还考虑了消失粘度极限。最后，我们提供并讨论了几个例子的扩散系数，改变符号，并表明我们的条件是满足了一个大类，他们在现实数据的对应。
英文摘要：
In this paper we consider an advection-diffusion equation, in one space dimension, whose diffusivity can be negative. Such equations arise in particular in the modeling of vehicular traffic flows or crowds dynamics, where a negative diffusivity simulates aggregation phenomena. We focus on traveling-wave solutions that connect two states whose diffusivity has different signs; under some geometric conditions we prove the existence, uniqueness (in a suitable class of solutions avoiding plateaus) and sharpness of the corresponding profiles. Such results are then extended to the case of end states where the diffusivity is positive but it becomes negative in some interval between them. Also the vanishing-viscosity limit is considered. At last, we provide and discuss several examples of diffusivities that change sign and show that our conditions are satisfied for a large class of them in correspondence of real data.
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