




Objectives of the project: We intend to investigate optimal control and stabilization problems related to three nonlinear parabolic systems: (1) a predatorprey system (with Holling, Beddingtonde Angelis or LotkaVolterra functional response to predation, which take into account logistic term, migration and agestructure), (2) a system describing the propagation of an epidemic with direct or indirect transmission, and (3) an economic growth model which takes into account the capital stock, the pollution and the human population dynamics. The optimal control problems will be related to the first and third models. We shall consider the optimal harvesting problem (with different forms of the production function) and even more general cost functions with a specific meaning and practical importance. Two aspects will be in our attention: the magnitude of the optimal control (when its support is given) and the spatial position and shape of the support of this control. The stabilization problems will be related to the first two models. We expect to establish the relationship between the zerostabilizability of one of the solution components for the above mentioned models and the magnitude of the principal eigenvalue of certain integrodifferential operators associated to the complement of the support of the control and to appropriate boundary conditions (which has to be found). We intend to 2013
2014
2015
2016
