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 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.
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Communicated by P. Newton.
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Colombo, R.M., Lécureux-Mercier, M. An Analytical Framework to Describe the Interactions Between Individuals and a Continuum. J Nonlinear Sci 22, 39–61 (2012). https://doi.org/10.1007/s00332-011-9107-0
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DOI: https://doi.org/10.1007/s00332-011-9107-0