A HAMILTON-JACOBI APPROACH TO JUNCTION PROBLEMS AND APPLICATION TO TRAFFIC FLOWS

被引：69

作者：

Imbert, Cyril ^{[1
,2
]}

Monneau, Regis ^{[3
]}

Zidani, Hasnaa ^{[4
,5
]}

机构：

[1] Univ Paris 09, CEREMADE, CNRS, UMR 7534, F-75775 Paris 16, France

[2] Ecole Normale Super, Dept Math & Applicat, UMR 8553, F-75230 Paris 5, France

[3] Univ Paris Est, Ecole Ponts ParisTech, CERM, F-77455 Marne La Vallee 2, France

[4] ENSTA ParisTech, F-75379 Paris 15, France

[5] INRIA Saclay, Commands INRIA Team, F-75379 Paris 15, France

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2013年 / 19卷 / 01期

关键词：

Hamilton-Jacobi equations; discontinuous Hamiltonians; viscosity solutions; optimal control; traffic problems; junctions; DISCONTINUOUS VISCOSITY SOLUTIONS; SCALAR CONSERVATION-LAWS; FLUX FUNCTION; EQUATIONS; UNIQUENESS; EXISTENCE; BELLMAN; WAVES;

D O I：

10.1051/cocv/2012002

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 is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to be new. They are applied to the study of some models arising in traffic flows. The techniques developed in the present article provide new powerful tools for the analysis of such problems.

引用

页码：129 / 166

页数：38

共 38 条

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Achdou Y., 2011, 18 IFAC WORLD C MIL

[2]

Achdou Y., 2010, 00503910 HAL

[3]

[Anonymous], 1994, MATH APPL

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