Effective transmission conditions for Hamilton-Jacobi equations defined on two domains separated by an oscillatory interface

DOI10.1016/J.MATPUR.2016.04.002zbMath1352.35212arXiv1506.02998OpenAlexW2962744799MaRDI QIDQ335872

Yves Achdou, Nicoletta Tchou, Salomé Oudet

Publication date: 3 November 2016

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.02998

zbMATH Keywords

homogenizationHamilton-Jacobi equationsdiscontinuous Hamiltonianeffective transmission conditionoscillatory interface

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Hamilton-Jacobi equations (35F21) PDEs in connection with control and optimization (35Q93)

Related Items (7)

Specified homogenization of a discrete traffic model leading to an effective junction condition ⋮ Quasi-convex Hamilton-Jacobi equations posed on junctions: the multi-dimensional case ⋮ Homogenization of a microscopic pedestrians model on a convergent junction ⋮ Homogenization of some periodic Hamilton-Jacobi equations with defects ⋮ Regularizing effect for unbounded flux-limited viscosity solutions of a discontinuous Hamilton-Jacobi equation on junction ⋮ Homogenization of a transmission problem with Hamilton-Jacobi equations and a two-scale interface. Effective transmission conditions ⋮ Hybrid Thermostatic Approximations of Junctions for Some Optimal Control Problems on Networks

Cites Work

• Hamilton-Jacobi equations constrained on networks
• A junction condition by specified homogenization and application to traffic lights
• Quasi-convex Hamilton-Jacobi equations posed on junctions: the multi-dimensional case
• A Bellman approach for two-domains optimal control problems in ℝ^N
• Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks
• A Bellman Approach for Regional Optimal Control Problems in $\mathbb{R}^N$
• The perturbed test function method for viscosity solutions of nonlinear PDE
• A Hamilton-Jacobi approach to junction problems and application to traffic flows
• Hamilton-Jacobi Equations on Networks as Limits of Singularly Perturbed Problems in Optimal Control: Dimension Reduction
• Hamilton–Jacobi equations for optimal control on junctions and networks
• Homogenization results for a deterministic multi-domains periodic control problem
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

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