Project Title:

Optimal Control and Stabilization of Nonlinear Parabolic Systems with State Constraints. Applications in Life Sciences and Economics

Project Code:

PN-II-ID-PCE-2012-4-0270

Project number:

68/02.09.2013

Supported by:

Romanian National Research Council and Executive Agency for Higher Education, Research, Development and Innovation, CNCS-UEFISCDI

Project Manager:

Prof. dr. Sebastian Aniţa

Thematic fields:

Main Sciences: Mathematics

Summary:

This project concerns the optimal control and stabilization of nonlinear parabolic systems with state constraints. The systems we will focus on are: (1) a predator-prey system (with different functional responses to predation),(2) a system describing the propagation of an epidemic, and (3) an economic growth model which takes into account the capital stock, the pollution stock and the human population dynamics. We will investigate optimal harvesting problems with different types of production functions related to the predator-prey system and to the economic growth model. We will investigate the magnitude of the optimal control and the optimal position and shape of the support of the control. We will also study the relationship between the stabilization to zero of one of the components of the first two models and the value of the principal eigenvalue to an appropriate integro-differential operator (corresponding to the complement of the support of the control and to appropriate boundary conditions) which is not selfadjoint. We will show that a large value of the principal eigenvalue leads to rapid stabilization to zero. We will also treat the maximizing of the principal eigenvalue with respect to the shape and position of the support of the control.