info:eu-repo/semantics/article
A nonlocal diffusion problem with a sharp free boundary
Fecha
2019-12Registro en:
Cortázar, Carmen; Quirós, Fernando; Wolanski, Noemi Irene; A nonlocal diffusion problem with a sharp free boundary; European Mathematical Society; Interfaces And Free Boundaries; 21; 4; 12-2019; 441-462
1463-9963
CONICET Digital
CONICET
Autor
Cortázar, Carmen
Quirós, Fernando
Wolanski, Noemi Irene
Resumen
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.