Objectives of the project:

We intend to investigate optimal control and stabilization problems related to three nonlinear parabolic systems:

(1) a predator-prey system (with Holling, Beddington-de Angelis or Lotka-Volterra functional response to predation, which take into account logistic term, migration and age-structure),

(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 zero-stabilizability of one of the solution components for the above mentioned models and the magnitude of the principal eigenvalue of certain integro-differential 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

1. Investigate the zero-stabilization of one of the components of a host-parasitoid (reaction-diffusion) system
2. Derive necessary conditions and sufficient conditions for zero-stabilizability (with state constraints) of some reaction-diffusion systems in population dynamics
3. Produce two scientific papers

2014

1. Investigate the relationship between the stabilization rate and the geometry of the support of the stabilizing control
2. Investigate some optimal control and stabilization problems in medicine, biology and economics (continued)
3. Produce two scientific papers

2015

1. Study the optimal control for a reaction-diffusion system and an economic growth model
2. Develop numerical methods to approximate the optimal control for optimal control problems related to reaction-diffusion system with migration and transport
3. Investigate some general optimal control problems related to reaction-diffusion systems in economics. Part I
4. Produce two scientific papers

2016

1. Study the optimal control and stabilization for reaction-diffusion models with age and size structure
2. Investigate some general optimal control problems related to reaction-diffusion systems in economics. Part II
3. Produce two scientific papers