On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations Associated with Nonlinear Boundary Conditions

Guy Barles, Hitoshi Ishii, Hiroyoshi Mitake

    Research output: Contribution to journalArticle

    9 Citations (Scopus)


    In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy-Neumann problems by using two fairly different methods: the first one relies only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the second one is an optimal control/dynamical system approach, named the "weak KAM approach", which requires the convexity of Hamiltonians and gives formulas for asymptotic solutions based on Aubry-Mather sets.

    Original languageEnglish
    Pages (from-to)515-558
    Number of pages44
    JournalArchive for Rational Mechanics and Analysis
    Issue number2
    Publication statusPublished - 2012 May


    ASJC Scopus subject areas

    • Analysis
    • Mechanical Engineering
    • Mathematics (miscellaneous)

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