Redlinger, Reinhard On Volterra’s population equation with diffusion. (English) Zbl 0593.92014 SIAM J. Math. Anal. 16, 135-142 (1985). 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. Cited in 1 ReviewCited in 24 Documents 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 Keywords:Volterra’s population equation with diffusion; single, isolated species; nonnegative solution; lower and upper solutions Citations:Zbl 0161.31901 PDFBibTeX XMLCite \textit{R. Redlinger}, SIAM J. Math. Anal. 16, 135--142 (1985; Zbl 0593.92014) Full Text: DOI