Special Session 106: Nonlocal and Local Interactions in Population Dynamics: Mathematical Analysis and Numerical Approaches.

On the regularity of optimal potentials for some elliptic control problems
Faustino Maestre
Universidad de Sevilla
Spain
Co-Author(s):    Giuseppe Buttazzo, Juan Casado-Diaz
Abstract:
In this work, we study an optimal control problem governed by an elliptic partial differential equation of Schrodinger type where the control is a potential. We consider a cost functional of integral type which involves the solution of the state equation and a penalization term of the control variable. It can represent biological models to control the size of a total population or the optimal location of resources. We focus on the regularity of optimal solutions, that no better than BV one can be expected. We present different examples, where bang-bang behavior of optimal solutions occur and we show some numerical simulations.