López-Gómez, Julián; Pardo San Gil, Rosa Coexistence in a simple food chain with diffusion. (English) Zbl 0763.92010 J. Math. Biol. 30, No. 7, 655-668 (1992). The global existence of classical positive solutions of a system of diffusion equations coupled in a linear tridiagonal manner by a source term and subject to linear mixed boundary conditions is shown. The coexistent states of the elliptic problem subject to homogeneous boundary conditions are investigated. Results are discussed in the context of a simple food chain — plant, herbivore and carnivore populations. Reviewer: N.Vulchanov (Gabrovo) Cited in 19 Documents MSC: 92D40 Ecology 35K57 Reaction-diffusion equations 35Q92 PDEs in connection with biology, chemistry and other natural sciences Keywords:plant; global existence of classical positive solutions; diffusion equations; linear mixed boundary conditions; coexistent states; elliptic problem; homogeneous boundary conditions; simple food chain; herbivore; carnivore populations PDFBibTeX XMLCite \textit{J. López-Gómez} and \textit{R. Pardo San Gil}, J. Math. Biol. 30, No. 7, 655--668 (1992; Zbl 0763.92010) Full Text: DOI