An Analytical Framework to Describe the Interactions Between Individuals and a Continuum
Analysis of PDEs
2015-05-20 v1
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.
Cite
@article{arxiv.1010.0978,
title = {An Analytical Framework to Describe the Interactions Between Individuals and a Continuum},
author = {Rinaldo M. Colombo and Magali Lécureux-Mercier},
journal= {arXiv preprint arXiv:1010.0978},
year = {2015}
}