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Evolution in a migrating population model

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Bąk W., Nadzieja T.

Applicationes Mathematicae

2012

tom 39

nr 3

305-313

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.

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1 Applicationes Mathematicae

1 Bąk W.

1 Nadzieja T.

1 2012

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Evolution in a migrating population model