
(AGENPARL) – SASSARI mar 09 maggio 2023
Seminario a cura della prof.ssa Claudia Anedda dell’Università di Cagliari.
La prof.ssa Claudia Anedda dell’Università di Cagliari, terrà un seminario dal titolo:
OPTIMAL LOCATION OF RESOURCES IN A POPULATION DYNAMICS MODEL IN HETEROGENEOUS ENVIRONMENTS
Abstract: We consider the indefinite weighted eigenvalue problem −?u = λmu in a bounded smooth domain Ω ⊂ RN , N ≥ 1, under homogeneous Dirichlet boundary conditions, where λ ∈ R and m(x) ∈ L∞(Ω) and we study the minimization of the principal positive eigenvalue λ1(m) when m varies in an appropriate class of bounded functions. This problem is related to the study of reaction-diffusion equations in mathematical ecology, in particular to the dynamics of a population inhabiting a heterogeneous environment Ω, where m(x), called the local growth rate, is positive on favourable habitats (for the survival of the population) and negative on unfavourable ones. We consider the weight m(x) as sum of two (or more) terms f1(x) + f2(x), where f1(x) and f2(x) can be interpreted as the spatial densities of two different types of resources; under the constraint that the total size of each resource is fixed, but their spatial arrangement is allowed to change, we show that there exists an optimal choice of f1(x) and f2(x) for the population to survive, and we find the form of the optimizers. The proof relies on some results about existence and characterization of a minimizer of λ1(m) in the context of the classes of rearrangements of measurable functions and on a particular property about these classes. The talk is based on joint work with Fabrizio Cuccu.
Per maggiori informazioni
Fonte/Source: https://www.uniss.it/uniss-comunica/eventi/seminario-dal-titolo-optimal-location-resources-population-dynamics-model-heterogeneous-environments