A dynamical approach to the large-time behavior of solutions to weakly coupled systems of Hamilton-Jacobi equations

DOI10.1016/j.matpur.2013.05.004zbMath1278.35020arXiv1208.6212OpenAlexW2963464840MaRDI QIDQ386257

Hung V. Tran, Hiroyoshi Mitake

Publication date: 9 December 2013

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

Full work available at URL: https://arxiv.org/abs/1208.6212

zbMATH Keywords

ergodic problem\(n\)-dimensional torusswitching cost problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Viscosity solutions to PDEs (35D40) Hamilton-Jacobi equations (35F21) PDEs in connection with control and optimization (35Q93) Initial value problems for systems of nonlinear first-order PDEs (35F55) Initial-boundary value problems for systems of nonlinear first-order PDEs (35F61)

Related Items (17)

The vanishing discount problem and viscosity Mather measures. 1: The problem on a torus ⋮ The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. I: Linear coupling ⋮ The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. II: Nonlinear coupling ⋮ Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems ⋮ Wellposedness of viscosity solutions to weakly coupled HJB equations under Hölder \textit{continuous conditions} ⋮ Weakly coupled systems of parabolic Hamilton-Jacobi equations with Caputo time derivative ⋮ Weak KAM theory for a weakly coupled system of Hamilton-Jacobi equations ⋮ Some results on the large-time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations ⋮ A new method for large time behavior of degenerate viscous Hamilton-Jacobi equations with convex Hamiltonians ⋮ A Lagrangian Approach to Weakly Coupled Hamilton--Jacobi Systems ⋮ Cycle characterization of the Aubry set for weakly coupled Hamilton–Jacobi systems ⋮ A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect ⋮ Weakly coupled mean-field game systems ⋮ Large-time behavior for obstacle problems for degenerate viscous Hamilton-Jacobi equations ⋮ Monotone systems involving variable-order nonlocal operators ⋮ A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton–Jacobi Equations ⋮ Weakly coupled systems of the infinity Laplace equations

Cites Work

• Convergence of a semi-discretization scheme for the Hamilton-Jacobi equation: a new approach with the adjoint method
• Large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations
• Homogenization of weakly coupled systems of Hamilton-Jacobi equations with fast switching rates
• Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean \(n\) space
• Remarks on the large time behavior of viscosity solutions of quasi-monotone weakly coupled systems of Hamilton--Jacobi equations
• Semicontinuous Viscosity Solutions For Hamilton–Jacobi Equations With Convex Hamiltonians
• A Generalized Dynamical Approach to the Large Time Behavior of Solutions of Hamilton--Jacobi Equations
• Viscosity Solutions for Weakly Coupled Systems of Hamilton-Jacobi Equations
• Viscosity solutions for monotone systems of second–order elliptic PDES
• Sur la convergence du semi-groupe de Lax-Oleinik
• Remarks on the long time behaviour of the solutions of hamilton-jacobi equations
• On the Large Time Behavior of Solutions of Hamilton--Jacobi Equations
• Aubry Sets for Weakly Coupled Systems of Hamilton--Jacobi Equations
• Homogenization of monotone systems of Hamilton-Jacobi equations
• Convergence to steady states or periodic solutions in a class of Hamilton-Jacobi equations

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