Convergence of the solutions of the discounted Hamilton-Jacobi equation: A counterexample

被引：10
|
作者：
Ziliotto, Bruno [1 ]
机构：
[1] Univ Paris 09, PSL Res Inst, CNRS, CEREMADE, Pl Marechal de Lattre de Tassigny, F-75016 Paris, France
来源：
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 128卷
关键词：
Hamilton-Jacobi equations; Viscosity solutions; Stochastic games; Zero-Sum games; REPEATED GAMES;
D O I：
10.1016/j.matpur.2019.04.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper provides a counterexample about the asymptotic behavior of the solutions of a discounted Hamilton-Jacobi equation, as the discount factor vanishes. The Hamiltonian of the equation is a 1-dimensional continuous and coercive Hamiltonian. (C) 2019 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：330 / 338
页数：9
相关论文
共 50 条
  • [1] Convergence of the solutions of the discounted Hamilton-Jacobi equation
    Davini, Andrea
    Fathi, Albert
    Iturriaga, Renato
    Zavidovique, Maxime
    INVENTIONES MATHEMATICAE, 2016, 206 (01) : 29 - 55
  • [2] Convergence of the solutions of the MFG discounted Hamilton-Jacobi equation
    Masoero, Marco
    arXiv, 2019,
  • [3] Convergence of the solutions of discounted Hamilton-Jacobi systems
    Davini, Andrea
    Zavidovique, Maxime
    ADVANCES IN CALCULUS OF VARIATIONS, 2021, 14 (02) : 193 - 206
  • [4] CONVERGENCE OF SOLUTIONS FOR SOME DEGENERATE DISCOUNTED HAMILTON-JACOBI EQUATIONS
    Zavidovique, Maxime
    ANALYSIS & PDE, 2022, 15 (05): : 1287 - 1311
  • [5] Convergence of the solutions of the nonlinear discounted Hamilton-Jacobi equation: The central role of Mather measures
    Chen, Qinbo
    Fathi, Albert
    Zavidovique, Maxime
    Zhang, Jianlu
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2024, 181 : 22 - 57
  • [6] Convergence of the solutions of the discounted Hamilton–Jacobi equationConvergence of the discounted solutions
    Andrea Davini
    Albert Fathi
    Renato Iturriaga
    Maxime Zavidovique
    Inventiones mathematicae, 2016, 206 : 29 - 55
  • [7] LIMIT OF THE INFINITE HORIZON DISCOUNTED HAMILTON-JACOBI EQUATION
    Iturriaga, Renato
    Sanchez-Morgado, Hector
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2011, 15 (03): : 623 - 635
  • [8] Physical solutions of the Hamilton-Jacobi equation
    Anantharaman, N
    Iturriaga, R
    Padilla, P
    Sánchez-Morgado, H
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2005, 5 (03): : 513 - 528
  • [9] GENERAL SOLUTIONS OF HAMILTON-JACOBI EQUATION
    EPSTEIN, ST
    AMERICAN JOURNAL OF PHYSICS, 1964, 32 (09) : 688 - &
  • [10] Generation of solutions of the Hamilton-Jacobi equation
    Torres del Castillo, G. F.
    REVISTA MEXICANA DE FISICA, 2014, 60 (01) : 75 - 79
12345