On some spectral problems arising in dynamic populations | Zendy

Antoine Henrot | Zendy; El Haj Laamri | Zendy; Didier Schmitt | Zendy

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On some spectral problems arising in dynamic populations

Author(s) -

Antoine Henrot,

El Haj Laamri,

Didier Schmitt

Publication year - 2012

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2012.11.2429

Subject(s) - dimension (graph theory) , intersection (aeronautics) , domain (mathematical analysis) , class (philosophy) , reaction–diffusion system , predation , natural (archaeology) , diffusion , optimal control , mathematics , mathematical optimization , computer science , mathematical economics , geography , pure mathematics , biology , ecology , cartography , mathematical analysis , artificial intelligence , physics , thermodynamics , archaeology

International audienceWe study a spectral problem related to a reaction-diffusion model where the preys and the predators do not live on the same area. We are interested in the optimal zone where the 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 size of domains

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