Control of the continuity equation with a non local flow

Rinaldo M. Colombo; Michael Herty; Magali Mercier

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 2, page 353-379
  • ISSN: 1292-8119

Abstract

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This paper focuses on the analytical properties of the 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 weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differentiability of solutions with respect to the initial datum and characterize this derivative. A necessary condition for the optimality of suitable integral functionals then follows.

How to cite

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Colombo, Rinaldo M., Herty, Michael, and Mercier, Magali. "Control of the continuity equation with a non local flow." ESAIM: Control, Optimisation and Calculus of Variations 17.2 (2011): 353-379. <http://eudml.org/doc/276335>.

@article{Colombo2011,
abstract = { This paper focuses on the analytical properties of the 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 weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differentiability of solutions with respect to the initial datum and characterize this derivative. A necessary condition for the optimality of suitable integral functionals then follows. },
author = {Colombo, Rinaldo M., Herty, Michael, Mercier, Magali},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control of the continuity equation; non-local flows; optimal control of the continuity equation; entropy solutions; pedestrian traffic model},
language = {eng},
month = {5},
number = {2},
pages = {353-379},
publisher = {EDP Sciences},
title = {Control of the continuity equation with a non local flow},
url = {http://eudml.org/doc/276335},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Colombo, Rinaldo M.
AU - Herty, Michael
AU - Mercier, Magali
TI - Control of the continuity equation with a non local flow
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2011/5//
PB - EDP Sciences
VL - 17
IS - 2
SP - 353
EP - 379
AB - This paper focuses on the analytical properties of the 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 weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differentiability of solutions with respect to the initial datum and characterize this derivative. A necessary condition for the optimality of suitable integral functionals then follows.
LA - eng
KW - Optimal control of the continuity equation; non-local flows; optimal control of the continuity equation; entropy solutions; pedestrian traffic model
UR - http://eudml.org/doc/276335
ER -

References

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