References
- Bardi M, Capuzzo DI. Optimal control and viscosity solutions of Hamilton–Jacobi–Bellman equations. Boston: Birkhauser; 1997.
- Crandall MG, Lions PL. Viscosity solutions of Hamilton–Jacobi equations. Trans Amer Math Soc. 1983;277:1–42. doi: 10.1090/S0002-9947-1983-0690039-8
- Hening A, Tran KQ, Phan TT, et al. Harvesting of interacting stochastic populations. J Math Biol. 2019;79:533–570. doi: 10.1007/s00285-019-01368-x
- Bang TV, Tien PT. On the existence, uniqueness and stability of β-viscosity solutions to a class of Hamilton–Jacobi equations in Banach spaces. Acta Math. (To appear). Available from: https://doi.org/10.1007/s40306-018-0287-7
- Crandall MG, Lions PL. Hamilton–Jacobi equations in infinite dimensions I. Uniqueness of viscosity solutions. J Funct Anal. 1985;62:379–398. doi: 10.1016/0022-1236(85)90011-4
- Li X, Yong J. Optimal Control theory for infinite dimensional systems. Boston: Birkhäuser; 1995.
- Borwein JM, Zhu QJ. Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity. SIAM J Control Optim. 1996;34:1568–1591. doi: 10.1137/S0363012994268801
- Aseev SM, Kryazhimskii AV. The Pontryagin maximum principle and optimal economic growth problems. Proc Steklov Inst Math. 2007;257:1–255. doi: 10.1134/S0081543807020010
- Baumeister J, Leit ao A, Silva GN. On the value function for nonautonomous optimal control problems with infinite horizon. Syst Control Lett. 2007;56:188–196. doi: 10.1016/j.sysconle.2006.08.011
- Hermosilla C, Zidani H. Infinite horizon problems on stratifiable state-constraints sets. J Differ Equ. 2015;258(4):1430–1460. doi:10.1016/j.jde.2014.11.001<hal-00955921v2>
- Achdou Y, Camilli F, Cutrì A, et al. Hamilton–Jacobi equations on networks. IFAC Proc Vol. 2011;44(1):2577–2582. doi: 10.3182/20110828-6-IT-1002.01084
- Achdou Y, Camilli F, Cutrì A, et al. Hamilton–Jacobi equations constrained on networks. NoDEA Nonlinear Differ Equ Appl. 2013;20(3):413–445. doi: 10.1007/s00030-012-0158-1
- Achdou Y, Oudet S, Tchou N. Hamilton–Jacobi equations for optimal control on junctions and networks. ESAIM Control Optim Calc Var. 2015;21(3):876–899. doi: 10.1051/cocv/2014054
- Barles G, Briani A, Chasseigne E. A Bellman approach for two-domains optimal control problems in RN. ESAIM Control Optim Calc Var. 2013;19(3):710–739. doi: 10.1051/cocv/2012030
- Barles G. An introduction to the theory of viscosity solutions for first-order Hamilton–Jacobi equations and applications. In: Loreti P, Tchou NA, editors. Hamilton–Jacobi equations: approximations, numerical analysis and applications. Heidelberg: Springer; 2013. p. 49–109. (volume 2074 of Lecture notes in math.).
- Khang DM. Hamilton–Jacobi equations for optimal control on networks with entry or exit costs. ESAIM Control Optim Calc Var. 2018. (In press). EDP Sciences. <hal-01548133v2>
- Lions PL, Souganidis P. Viscosity solutions for junctions: well posedness and stability. Atti Accad Naz Lincei Rend Lincei Mat Appl. 2016;27(4):535–545. doi: 10.4171/RLM/747
- Oudet S. Hamilton–Jacobi equations for optimal control on multidimensional junctions. Preprint (2014). arXiv: 1412.2679