Geodesic
Control of the continuity equation with a non local flow
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 2, pp. 353-379

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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.

DOI : 10.1051/cocv/2010007
Classification : 35L65, 49K20, 93C20
Keywords: optimal control of the continuity equation, non-local flows 
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     author = {Colombo, Rinaldo M. and Herty, Michael and Mercier, Magali},
     title = {Control of the continuity equation with a non local flow},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {353--379},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {2},
     year = {2011},
     doi = {10.1051/cocv/2010007},
     mrnumber = {2801323},
     zbl = {1232.35176},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010007/}
}
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Colombo, Rinaldo M.; Herty, Michael; Mercier, Magali. Control of the continuity equation with a non local flow. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 2, pp. 353-379. doi: 10.1051/cocv/2010007

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