Discontinuous Solutions of Hamilton-Jacobi Equations on Networks

2017
Publication type:
Paper in peer-reviewed journals
Journal:
Journal of Differential Equations
Keywords :
Control problem on networks; state constraint problems; stratified structure; Hamilton-Jacobi equations equations; nonsmooth analysis;
Abstract:
This paper studies optimal control problems on networks without controllability assumptions at the junctions. The Value Function associated with the control problem is characterized as solution to a system of Hamilton-Jacobi equations with appropriate junction conditions. The novel feature of the result lies in that the controllability conditions are not needed and the characterization remains valid even when the Value Function is not continuous.
BibTeX:
@article{Gra-Her-Zid-2017,
    author={Philip Jameson Graber and Cristopher Hermosilla and Hasnaa 
           Zidani },
    title={Discontinuous Solutions of Hamilton-Jacobi Equations on 
           Networks },
    doi={10.1016/j.jde.2017.08.040 },
    journal={Journal of Differential Equations },
    year={2017 },
}