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arXiv · 1010.0978

An Analytical Framework to Describe the Interactions Between Individuals and a Continuum

Rinaldo M. Colombo·Magali Lécureux-Mercier
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Abstract

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.

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Rinaldo M. Colombo, Magali Lécureux-Mercier. 2010-10-05. An Analytical Framework to Describe the Interactions Between Individuals and a Continuum. https://doi.org/10.1007/s00332-011-9107-0

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