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All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 88 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 88
Number of page(s) 35
DOI https://doi.org/10.1051/cocv/2024077
Published online 19 November 2024
  1. B. Andreianov, K.H. Karlsen and N.H. Risebro, A theory of L1-dissipative solvers for scalar conservation laws with discontinuous flux. Arch. Ration. Mech. Anal. 201 (2011) 27–86. [Google Scholar]
  2. A. Bayen, M.L. Delle Monache, M. Garavello, P. Goatin and B. Piccoli, Control Problems for Conservation Laws with Traffic Applications: Modeling, Analysis, and Numerical Methods. Springer Nature (2022). [CrossRef] [Google Scholar]
  3. A. Bressan, S. Čanić, M. Garavello, M. Herty and B. Piccoli, Flows on networks: recent results and perspectives. EMS Surv. Math. Sci. 1 (2014) 47–111. [CrossRef] [MathSciNet] [Google Scholar]
  4. B. Piccoli, Control of multi-agent systems: results, open problems, and applications. Open Math. 21 (2023) 20220585. [CrossRef] [Google Scholar]
  5. A. Bressan and K. Han, Optima and equilibria for a model of traffic flow. SIAM J. Math. Anal. 43 (2011) 2384–2417. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Bressan and K. Han, Nash equilibria for a model of traffic flow with several groups of drivers. ESAIM: Control Optim. Calc. Var. 18 (2012) 969–986. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  7. A. Bressan and K. Han, Existence of optima and equilibria for traffic flow on networks. Networks Heterog. Media 8 (2013) 627–648. [CrossRef] [MathSciNet] [Google Scholar]
  8. A. Bressan and K.T. Nguyen, Optima and equilibria for traffic flow on networks with backward propagating queues. Networks Heterog. Media 10 (2015) 717–748. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Cascone, C. D’Apice, B. Piccoli and L. Rarità, Optimization of traffic on road networks. Math. Models Methods Appl. Sci. 17 (2007) 1587–1617. [CrossRef] [MathSciNet] [Google Scholar]
  10. R.M. Colombo, P. Goatin and M.D. Rosini, On the modelling and management of traffic. ESAIM: Math. Model. Numer. Anal. 45 (2011) 853–872. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  11. M. Gugat, M. Herty, A. Klar and G. Leugering, Optimal control for traffic flow networks. J. Optim. Theory Appl. 126 (2005) 589–616. [CrossRef] [MathSciNet] [Google Scholar]
  12. M. Herty and A. Klar, Modeling, simulation, and optimization of traffic flow networks. SIAM J. Sci. Comput. 25 (2003) 1066–1087. [CrossRef] [MathSciNet] [Google Scholar]
  13. L. Tumash, C. Canudas-de-Wit and M.L. Delle Monache, Boundary control design for traffic with nonlinear dynamics. IEEE Trans. Automatic Control 67 (2021) 1301–1313. [Google Scholar]
  14. R.M. Colombo and A. Groli, Minimising stop and go waves to optimise traffic flow. Appl. Math. Lett. 17 (2004) 697–701. [CrossRef] [MathSciNet] [Google Scholar]
  15. F. Ancona, A. Cesaroni, G.M. Coclite and M. Garavello, On the optimization of conservation law models at a junction with inflow and flow distribution controls. SIAM J. Control Optim. 56 (2018) 3370–3403. [Google Scholar]
  16. C. Imbert, R. Monneau and H. Zidani, A Hamilton–Jacobi approach to junction problems and application to traffic flows. ESAIM Control Optim. Calc. Var. 19 (2013) 129–166. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  17. P. Cardaliaguet, N. Forcadel and R. Monneau, A class of germs arising from homogenization in traffic flow on junctions. J. Hyperbolic Differ. Equ. 21 (2024) 189–254. [CrossRef] [MathSciNet] [Google Scholar]
  18. C. Imbert and R. Monneau, Flux-limited solutions for quasi-convex Hamilton–Jacobi equations on networks. Ann. Sci. Éc. Norm. Supér. 50 (2017) 357–448. [CrossRef] [MathSciNet] [Google Scholar]
  19. Y. Achdou, S. Oudet and N. Tchou, Hamilton–Jacobi equations for optimal control on junctions and networks. ESAIM: Control Optim. Calc. Var. 21 (2015) 876–899. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  20. G. Barles and E. Chasseigne, An illustrated guide of the modern approaches of Hamilton–Jacobi equations and control problems with discontinuities, Birkhaüser (2024). [CrossRef] [Google Scholar]
  21. P.-L. Lions and P. Souganidis, Viscosity solutions for junctions: well posedness and stability. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 27 (2016) 535–545. [MathSciNet] [Google Scholar]
  22. P.-L. Lions and P. Souganidis, Well-posedness for multi-dimensional junction problems with Kirchoff-type conditions. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 28 (2017) 807–816. [MathSciNet] [Google Scholar]
  23. P. Cardaliaguet, N. Forcadel, T. Girard and R. Monneau, Conservation law and Hamilton-Jacobi equations on a junction: the convex case. Discrete Contin. Dyn. Syst.-A 44 (2024) 3920–3961. [CrossRef] [MathSciNet] [Google Scholar]

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