A comparison among various notions of viscosity solution for Hamilton-Jacobi equations on networks

DOI10.1016/j.jmaa.2013.05.015zbMath1319.49039arXiv1301.0194OpenAlexW2963976520MaRDI QIDQ2257513

Fabio Camilli, Claudio Marchi

Publication date: 25 February 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.0194

zbMATH Keywords

networksHamilton-Jacobi equationsviscosity solutions

Mathematics Subject Classification ID

Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Viscosity solutions to PDEs (35D40) Hamilton-Jacobi equations (35F21) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (16)

Hamilton-Jacobi equations for optimal control on multidimensional junctions with entry costs ⋮ Global results for eikonal Hamilton-Jacobi equations on networks ⋮ The Lax-Oleinik semigroup on graphs ⋮ Hamilton-Jacobi equations for optimal control on networks with entry or exit costs ⋮ Junction conditions for finite horizon optimal control problems on multi-domains with continuous and discontinuous solutions ⋮ Microscopic derivation of a traffic flow model with a bifurcation ⋮ A combinatorial representation for the invariant measure of diffusion processes on metric graphs ⋮ A flame propagation model on a network with application to a blocking problem ⋮ A Semi-Lagrangian Scheme for Hamilton--Jacobi--Bellman Equations on Networks ⋮ Hamilton-Jacobi equations on graph and applications ⋮ A discrete Hughes model for pedestrian flow on graphs ⋮ A piecewise deterministic Markov toy model for traffic/maintenance and associated Hamilton-Jacobi integrodifferential systems on networks ⋮ Hybrid Thermostatic Approximations of Junctions for Some Optimal Control Problems on Networks ⋮ Hamilton-Jacobi Equations on Networks as Limits of Singularly Perturbed Problems in Optimal Control: Dimension Reduction ⋮ A general comparison principle for Hamilton Jacobi Bellman equations on stratified domains ⋮ Eikonal equations on the Sierpinski gasket

Cites Work

• Hamilton-Jacobi equations constrained on networks
• The vanishing viscosity limit for Hamilton-Jacobi equations on networks
• Viscosity solutions of eikonal equations on topological networks
• A Regularity Result for Viscosity Solutions of Hamilton-Jacobi Equations in One Space Dimensions
• A Hamilton-Jacobi approach to junction problems and application to traffic flows
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

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