On some spectral problems arising in dynamic populations

Antoine Henrot (1, 2) , El Haj Laamri (2) , Didier Schmitt (2)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 IECN - Institut Élie Cartan de Nancy

We 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.

Mots clés: Non self-adjoint spectral problem; Reaction-diffusion systems; Shape optimization

Domaines: Equations aux dérivées partielles [math.AP]

Antoine Henrot, El Haj Laamri, Didier Schmitt. On some spectral problems arising in dynamic populations. Communications on Pure and Applied Analysis, 2012, 11 (6), pp.2429-2443. ⟨10.3934/cpaa.2012.11.2429⟩. ⟨hal-00585251v2⟩