A nonlocal diffusion problem with a sharp free boundary

被引：21

作者：

Cortazar, Carmen ^{[1
]}

Quiros, Fernando ^{[2
]}

Wolanski, Noemi ^{[3
,4
]}

机构：

[1] Pontificia Univ Catolica Chile, Dept Matemat, Santiago, Chile

[2] Univ Autonoma Madrid, Dept Matemat, Madrid 28049, Spain

[3] Univ Buenos Aires, Dept Matemat, FCEyN, Buenos Aires, DF, Argentina

[4] Consejo Nacl Invest Cient & Tecn, IMAS, RA-1428 Buenos Aires, DF, Argentina

来源：

INTERFACES AND FREE BOUNDARIES | 2019年 / 21卷 / 04期

关键词：

Nonlocal diffusion; free boundary problems; population dynamics; EQUATION;

D O I：

10.4171/IFB/430

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：441 / 462

页数：22

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