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Coexistence in a simple food chain with diffusion. (English) Zbl 0763.92010

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.

MSC:

92D40 Ecology
35K57 Reaction-diffusion equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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