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Interfaces and Free Boundaries

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Volume 21, Issue 4, 2019, pp. 441–462
DOI: 10.4171/IFB/430

Published online: 2019-12-18

A nonlocal diffusion problem with a sharp free boundary

Carmen Cortázar[1], Fernando Quirós[2] and Noemi Wolanski[3]

(1) Pontificia Universidad Católica de Chile, Santiago de Chile, Chile
(2) Universidad Autónoma de Madrid, Spain
(3) CONICET and Universidad de Buenos Aires, Argentina

We introduce and analyze a nonlocal free boundary problem which may be of interest to describe the spreading of populations in hostile environments. The rate of growth of the volume of the region occupied by the population is proportional to the rate at which the total population decreases. We prove existence and uniqueness for the problem posed on the line, on the half-line with constant Dirichlet data, and in the radial case in several dimensions.We also describe the asymptotic behaviour of both the solution and its free boundary.

Keywords: Nonlocal diffusion, free boundary problems, population dynamics

Cortázar Carmen, Quirós Fernando, Wolanski Noemi: A nonlocal diffusion problem with a sharp free boundary. Interfaces Free Bound. 21 (2019), 441-462. doi: 10.4171/IFB/430