On some spectral problems arising in dynamic populations

Antoine Henrot; El-Haj Laamri; Didier Schmitt

doi:10.3934/cpaa.2012.11.2429

Article Contents

2012, Volume 11, Issue 6: 2429-2443. Doi: 10.3934/cpaa.2012.11.2429

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On some spectral problems arising in dynamic populations

1.
Institut Elie Cartan, Nancy Université - CNRS, B.P. 239, 54 506 Vandoeuvre-les-Nancy
2.
Institut Elie Cartan, Nancy Université - CNRS, B.P. 239, 54 506 Vandoeuvre-lès-Nancy

Received: January 31, 2011

Revised: January 31, 2011

Published: October 2012

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Abstract

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.

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Mathematics Subject Classification: Primary: 49J20; Secondary: 35P15, 92D25.

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References

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