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On Volterra’s population equation with diffusion. (English) Zbl 0593.92014

Summary: In this paper Volterra’s population equation with diffusion for a single, isolated species \(u\) is considered. Generalizing a result of R. K. Miller [SIAM J. Appl. Math. 14, 446-452 (1966; Zbl 0161.31901)] it is shown that every nonnegative solution \(u\not\equiv 0\) tends, as \(t\to \infty\), to a spatially homogeneous distribution \(u^*\), independent of the initial distribution of \(u\). For proof, a recursively defined sequence of pairs of lower and upper solutions is used.

MSC:

92D25 Population dynamics (general)
45K05 Integro-partial differential equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations

Citations:

Zbl 0161.31901
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