FLUX-LIMITED SOLUTIONS FOR QUASI-CONVEX HAMILTON-JACOBI EQUATIONS ON NETWORKS

被引：0

作者：

Imbert, Cyril ^{[1
]}

Monneau, Regis ^{[2
]}

机构：

[1] Ecole Natl Super Paris, Dept Math & Applicat, CNRS, UMR 8553, 45 Rue Ulm, F-75230 Paris 5, France

[2] Univ Paris Est, CERMICS, ENPC, 6-8 Ave Blaise Pascal, F-77455 Marne La Vallee 2, France

来源：

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE | 2017年 / 50卷 / 02期

关键词：

VISCOSITY SOLUTIONS; DISCONTINUOUS COEFFICIENTS; DIFFERENTIAL-GAMES; STRATIFIED DOMAINS; EIKONAL EQUATIONS; CONSERVATION-LAWS; STATE CONSTRAINTS; BELLMAN EQUATIONS; METRIC-SPACES; R-N;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Hamilton-Jacobi equations on networks in the case where Hamiltonians are quasi-convex with respect to the gradient variable and can be discontinuous with respect to the space variable at vertices. First, we prove that imposing a general vertex condition is equivalent to imposing a specific one which only depends on Hamiltonians and an additional free parameter, the flux limiter. Second, a general method for proving comparison principles is introduced. This method consists in constructing a vertex test function to be used in the doubling variable approach. With such a theory and such a method in hand, we present various applications, among which a very general existence and uniqueness result for quasi-convex Hamilton-Jacobi equations on networks.

引用

页码：357 / 448

页数：92