Xu, Fei; Hou, Yan; Lin, Zhi Gui Time delay parabolic system in a predator-prey model with stage structure. (Chinese. English summary) Zbl 1124.35330 Acta Math. Sin. 48, No. 6, 1121-1130 (2005). Summary: In this paper, a two-species predator-prey system is discussed, the dynamics of coupled system of semilinear parabolic equations with time delays is investigated using upper and lower solutions and the associated monotone iterations. The asymptotic behavior of solutions and the negative effect of stage structure on the permanence of populations are given. Cited in 1 Document MSC: 35K57 Reaction-diffusion equations 35B40 Asymptotic behavior of solutions to PDEs 35K50 Systems of parabolic equations, boundary value problems (MSC2000) 35Q80 Applications of PDE in areas other than physics (MSC2000) 92D25 Population dynamics (general) Keywords:reaction diffusion system; stage structure; time delay PDFBibTeX XMLCite \textit{F. Xu} et al., Acta Math. Sin. 48, No. 6, 1121--1130 (2005; Zbl 1124.35330)