Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians

Naoyuki Ichihara, Hitoshi Ishii

    Research output: Contribution to journalArticle

    21 Citations (Scopus)

    Abstract

    We investigate the long-time behavior of viscosity solutions of Hamilton-Jacobi equations in ℝn with convex and coercive Hamiltonians and give three general criteria for the convergence of solutions to asymptotic solutions as time goes to infinity. We apply the criteria to obtain more specific sufficient conditions for the convergence to asymptotic solutions and then examine them with examples. We take a dynamical approach, based on tools from weak KAM theory such as extremal curves, Aubry sets and representation formulas for solutions, for these investigations.

    Original languageEnglish
    Pages (from-to)383-419
    Number of pages37
    JournalArchive for Rational Mechanics and Analysis
    Volume194
    Issue number2
    DOIs
    Publication statusPublished - 2009 Sep

    Fingerprint

    Hamiltonians
    Asymptotic Solution
    Hamilton-Jacobi Equation
    Long-time Behavior
    Behavior of Solutions
    KAM Theory
    Convergence of Solutions
    Representation Formula
    Viscosity Solutions
    Infinity
    Viscosity
    Curve
    Sufficient Conditions

    ASJC Scopus subject areas

    • Analysis
    • Mechanical Engineering
    • Mathematics (miscellaneous)

    Cite this

    Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians. / Ichihara, Naoyuki; Ishii, Hitoshi.

    In: Archive for Rational Mechanics and Analysis, Vol. 194, No. 2, 09.2009, p. 383-419.

    Research output: Contribution to journalArticle

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