We consider a model of migrating population occupying a compact domain Ω in the plane. We assume the Malthusian growth of the population at each point x ∈ Ω and that the mobility of individuals depends on x ∈ Ω. The evolution of the probability density u(x,t) that a randomly chosen individual occupies x ∈ Ω at time t is described by the nonlocal linear equation , where φ(x) is a given function characterizing the mobility of individuals living at x. We show that the asymptotic behaviour of u(x,t) as t → ∞ depends on the properties of φ in the vicinity of its zeros.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-5,
author = {W\l odzimierz B\k ak and Tadeusz Nadzieja},
title = {Evolution in a migrating population model},
journal = {Applicationes Mathematicae},
volume = {39},
year = {2012},
pages = {305-313},
zbl = {1251.35170},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-5}
}
Włodzimierz Bąk; Tadeusz Nadzieja. Evolution in a migrating population model. Applicationes Mathematicae, Tome 39 (2012) pp. 305-313. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-5/