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On some spectral problems arising in dynamic populations

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  • We study a spectral problem related to a reaction-diffusion model where preys and predators do not live on the same area. We are interested in the optimal zone where a control should take place. First, we prove existence of an optimal domain in a natural class. Then, it seems plausible that the optimal domain is localized in the intersection of the living areas of the two species. We prove this fact in one dimension for small sized domains.
    Mathematics Subject Classification: Primary: 49J20; Secondary: 35P15, 92D25.


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