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

Guy Barles*, Hitoshi Ishii, Hiroyoshi Mitake

*この研究の対応する著者

    研究成果: Article査読

    12 被引用数 (Scopus)

    抄録

    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.

    本文言語English
    ページ(範囲)515-558
    ページ数44
    ジャーナルArchive for Rational Mechanics and Analysis
    204
    2
    DOI
    出版ステータスPublished - 2012 5月

    ASJC Scopus subject areas

    • 分析
    • 機械工学
    • 数学(その他)

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