A nonlocal diffusion problem with a sharp free boundary
Carmen Cortázar
Pontificia Universidad Católica de Chile, Santiago de Chile, ChileFernando Quirós
Universidad Autónoma de Madrid, SpainNoemi Wolanski
CONICET and Universidad de Buenos Aires, Argentina
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Abstract
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.
Cite this article
Carmen Cortázar, Fernando Quirós, Noemi Wolanski, A nonlocal diffusion problem with a sharp free boundary. Interfaces Free Bound. 21 (2019), no. 4, pp. 441–462
DOI 10.4171/IFB/430