Convergence to time-periodic solutions in Hamilton-Jacobi equations on the circle

2003/03/27 by Patrick Bernard, Jean-Michel Roquejoffre, Jean‐Michel Roquejoffre +2
Mathematics · Physics and Astronomy · #35F25 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #math.AP #math.DS #math.OC #msc:35F25

paper · pdf · doi:10.48550/arxiv.math/0303351

openalex publication_date 2003/03/27 · arxiv created 2003/06/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is to give a simple proof of the convergence to time-periodic states of the solutions of time-periodic Hamilton-Jacobi equations on the circle with convex Hamiltonian. Note that the period of the limiting solutions may be greater than the period of the Hamiltonian.

Citations

• Action minimizing invariant measures for positive definite Lagrangian systems

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