Control of the Continuity Equation with a Non Local Flow
Analysis of PDEs
2009-02-17 v1 Optimization and Control
Abstract
This paper focuses on the optimal control of weak (i.e. in general non smooth) solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows. To this aim, we prove the well posedness of a class of equations comprising these models. In particular, we prove the differentiability of solutions with respect to the initial datum and characterize its derivative. A necessary condition for the optimality of suitable integral functionals then follows.
Cite
@article{arxiv.0902.2623,
title = {Control of the Continuity Equation with a Non Local Flow},
author = {Rinaldo M. Colombo and Michael Herty and Magali Mercier},
journal= {arXiv preprint arXiv:0902.2623},
year = {2009}
}