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Pré-Publication, Document De Travail Année : 2010

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

Résumé

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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Dates et versions

hal-00523068 , version 1 (05-10-2010)

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Rinaldo M. Colombo, Magali Lécureux-Mercier. An Analytical Framework to Describe the Interactions Between Individuals and a Continuum. 2010. ⟨hal-00523068⟩
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