Optimization in structure population models through the Escalator Boxcar Train^{★,★★,★★★}

¹ University of Brescia, 25121 Brescia, BS, Italie
² University of Warsaw, 00-927 Warszawa, Pologne
pgwiazda@mimuw.edu.pl; mrosinska@pzh.gov.pl

^a Corresponding author: rinaldo.colombo@unibs.it

Received: 8 January 2016
Revised: 7 November 2016
Accepted: 12 January 2017

Abstract

The Escalator Boxcar Train (EBT) is a tool widely used in the study of balance laws motivated by structure population dynamics. This paper proves that the approximate solutions defined through the EBT converge to exact solutions. Moreover, this method is rigorously shown to be effective also in computing optimal controls. As preliminary results, the well posedness of classes of PDEs and of ODEs comprising various biological models is also obtained. A specific application to welfare policies illustrates the whole procedure.