Evolution in a migrating population model

Włodzimierz Bąk, and Tadeusz Nadzieja. "Evolution in a migrating population model." Applicationes Mathematicae 39.3 (2012): 305-313. <http://eudml.org/doc/279944>.

@article{WłodzimierzBąk2012,
abstract = {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 $u_t = ∫_Ω φ(y)u(y,t)dy - φ(x)u(x,t)$, 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.},
author = {Włodzimierz Bąk, Tadeusz Nadzieja},
journal = {Applicationes Mathematicae},
keywords = {nonlocal differential equation; evolution of population density},
language = {eng},
number = {3},
pages = {305-313},
title = {Evolution in a migrating population model},
url = {http://eudml.org/doc/279944},
volume = {39},
year = {2012},
}

TY - JOUR
AU - Włodzimierz Bąk
AU - Tadeusz Nadzieja
TI - Evolution in a migrating population model
JO - Applicationes Mathematicae
PY - 2012
VL - 39
IS - 3
SP - 305
EP - 313
AB - 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 $u_t = ∫_Ω φ(y)u(y,t)dy - φ(x)u(x,t)$, 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.
LA - eng
KW - nonlocal differential equation; evolution of population density
UR - http://eudml.org/doc/279944
ER -