Internal stabilizability for a reaction-diffusion problem modeling a predator-prey system. (English summary) Nonlinear Anal. 61 (2005), no. 4, 491–501. Summary: “In this work we consider a 2 × 2 system of semilinear partial differential equations of parabolic type describing interactions between a prey population and a predator population, featuring a Holling-type II functional response to predation. We address the question of stabilizing the predator population to zero, upon using a suitable internal control supported on a small subdomain ω of the whole spatial domain Ω, and acting on predators. We give necessary and sufficient conditions for this stabilizability result to hold.
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