On a long range segregation model
Luis A. Caffarelli
University of Texas at Austin, USAStefania Patrizi
University of Texas at Austin, USAVeronica Quitalo
Purdue University, West Lafayette, USA
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Abstract
In this work we study the properties of segregation processes modeled by a family of equations
where is a non-local factor that takes into consideration the values of the functions in a full neighborhood of We consider as a model problem
where is a small parameter and is for instance
Here is the unit ball centered at with respect to a smooth, uniformly convex norm of . Heuristically, this will force the populations to stay at -distance 1, one from each other, as .
Cite this article
Luis A. Caffarelli, Stefania Patrizi, Veronica Quitalo, On a long range segregation model. J. Eur. Math. Soc. 19 (2017), no. 12, pp. 3575–3628
DOI 10.4171/JEMS/747