# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## Evolution in a migrating population model

### Tom 39 / 2012

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

#### Streszczenie

We consider a model of migrating population occupying a compact domain $\varOmega$ 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.

#### Autorzy

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