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

Rinaldo M. Colombo (1) , Magali Lécureux-Mercier (2)

1 UniBs - Università degli Studi di Brescia = University of Brescia
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Mots clés: Mixed P.D.E.–O.D.E. Problems; Conservation Laws; Ordinary Differential Equations

Domaines: Equations aux dérivées partielles [math.AP]

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