一个描述个体与连续体相互作用的分析框架
An Analytical Framework to Describe the Interactions Between Individuals and a Continuum
摘要：
我们考虑一个离散集的个人代理与连续。例子可能是一个捕食者面对一大群猎物，或几个牧羊犬驱赶一群羊。从分析上讲，这些情况可以通过一个常微分方程系统与几个空间维度中的标量守恒律耦合来描述。本文对所得的柯西问题提供了一个完整的适定性理论。几个应用程序被认为是详细和数值积分提供。
英文摘要：
We consider a discrete set of individual agents interacting with a continuum. Examples might be a predator facing a huge group of preys, or a few shepherd dogs driving a herd of sheeps. Analytically, these situations can be described through a system of ordinary differential equations coupled with a scalar conservation law in several space dimensions. This paper provides a complete well posedness theory for the resulting Cauchy problem. A few applications are considered in detail and numerical integrations are provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
