CONTROL OF THE CONTINUITY EQUATION WITH A NON LOCAL FLOW

被引：73

作者：

Colombo, Rinaldo M. ^{[1
]}

Herty, Michael ^{[2
]}

Mercier, Magali ^{[3
]}

机构：

[1] Univ Brescia, Dept Math, I-25133 Brescia, Italy

[2] Rhein Westfal TH Aachen, D-52056 Aachen, Germany

[3] Univ Lyon 1, Ecole Cent Lyon, INSA Lyon, Inst Camille Jordan,CNRS UMR 5208, F-69622 Villeurbanne, France

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2011年 / 17卷 / 02期

关键词：

Optimal control of the continuity equation; non-local flows; HYPERBOLIC CONSERVATION-LAWS; DISCONTINUOUS SOLUTIONS; BALANCE LAWS; MODEL; OPTIMIZATION; DYNAMICS;

D O I：

10.1051/cocv/2010007

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：353 / 379

页数：27

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