Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean n space

Hitoshi Ishii

    Research output: Contribution to journalArticle

    45 Citations (Scopus)


    We study the large time behavior of solutions of the Cauchy problem for the Hamilton-Jacobi equation ut + H (x, D u) = 0 in Rn × (0, ∞), where H (x, p) is continuous on Rn × Rn and convex in p. We establish a general convergence result for viscosity solutions u (x, t) of the Cauchy problem as t → ∞.

    Original languageEnglish
    Pages (from-to)231-266
    Number of pages36
    JournalAnnales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
    Issue number2
    Publication statusPublished - 2008 Mar



    • Asymptotic solutions
    • Hamilton-Jacobi equations
    • Large time behavior
    • Weak KAM theory

    ASJC Scopus subject areas

    • Analysis

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