Processing math: 0%

Wykorzystujemy pliki cookies aby ułatwić Ci korzystanie ze strony oraz w celach analityczno-statystycznych.

A+ CATEGORY SCIENTIFIC UNIT

Evolution in a migrating population model

Volume 39 / 2012

Włodzimierz Bąk, Tadeusz Nadzieja Applicationes Mathematicae 39 (2012), 305-313 MSC: 35R09, 92D25. DOI: 10.4064/am39-3-5

Abstract

We consider a model of migrating population occupying a compact domain in the plane. We assume the Malthusian growth of the population at each point x\in \varOmega and that the mobility of individuals depends on x\in \varOmega . The evolution of the probability density u(x,t) that a randomly chosen individual occupies x\in \varOmega at time t is described by the nonlocal linear equation u_t=\int _\varOmega \varphi (y)u(y,t) \, dy-\varphi (x)u(x,t), where \varphi (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\to \infty depends on the properties of \varphi in the vicinity of its zeros.

Authors

  • Włodzimierz BąkInstytut Matematyki i Informatyki
    Uniwersytet Opolski
    Oleska 48
    45-052 Opole, Poland
    e-mail
  • Tadeusz NadziejaInstytut Matematyki i Informatyki
    Uniwersytet Opolski
    Oleska 48
    45-052 Opole, Poland
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image