On Volterra’s Population Equation with Diffusion
Copyright policy )On Volterra’s Population Equation with Diffusion
Summary: In this paper Volterra's population equation with diffusion for a single, isolated species \(u\) is considered. Generalizing a result of \textit{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.
Integro-partial differential equations, Population dynamics (general), Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, single, isolated species, lower and upper solutions, Nonlinear boundary value problems for linear elliptic equations, nonnegative solution, Volterra's population equation with diffusion
Integro-partial differential equations, Population dynamics (general), Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, single, isolated species, lower and upper solutions, Nonlinear boundary value problems for linear elliptic equations, nonnegative solution, Volterra's population equation with diffusion
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).36 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!