# 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

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topColombo, 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 -

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