An Analytical Framework to Describe the Interactions Between Individuals and a Continuum
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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 sheep. 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.
KeywordsMixed P.D.E.–O.D.E. problems Conservation laws Ordinary differential equations
Mathematics Subject Classification (2000)35L65 34A12 37N99
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