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Coexistence, stability, and limiting behavior in a one-predator-two-prey model. (English) Zbl 0846.35067
Summary: This paper considers a reaction-diffusion system that models the situation in which a predator feeds on two prey species. The existence of a positive steady-state solution as well as the existence and stability of various semitrivial steady-state solutions is obtained in terms of the natural growth rates of the three species. The present paper also gives some explicit information on the limiting behavior of the time-dependent solution to these steady states.

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
92D25 Population dynamics (general)
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