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Persistence and extinction in two species reaction-diffusion systems with delays. (English) Zbl 0936.35092
Two species predator- prey and competition reaction-diffusion systems with delays are considered. First uniform persistence criteria for these two types of systems are established.
Current results on this subject are obtained by using a comparison argument. The abstract persistence theory and the infinite-dimensional dissipative system theory is used. In addition the global extinction of these systems are established, that is, the global attractivity of the boundary equilibria is studied.

MSC:
35K57 Reaction-diffusion equations
35R10 Functional partial differential equations
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