Discontinuous solutions of Hamilton-Jacobi equations on networks *

Philip Jameson Graber, Cristopher Hermosilla and Hasnaa Zidani

2017

Publication type:

Paper in peer-reviewed journals

Journal:

Journal of Differential Equations, vol. 263 (12), pp. 8418-8466

Publisher:

Elsevier

External link:

https://authors.elsevier.com/c/1VvFG50j-ZtTe

DOI:

10.1016/j.jde.2017.08.040

HAL:

hal-01363628

Keywords :

nonsmooth analysis; state constraint problems; Hamilton-Jacobi equations equations; stratified structure; Control problem on networks;

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 },
    volume={263 (12) },
    pages={8418--8466},
}