Asymptotic solutions of Hamilton-Jacobi equations with semi-periodic Hamiltonians

Naoyuki Ichihara, Hitoshi Ishii*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    22 Citations (Scopus)


    We study the long time behavior of viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations in ℝn. We prove that if the Hamiltonian H(x, p) is coercive and strictly convex in a mild sense in p and upper semi-periodic in x, then any solution of the Cauchy problem "converges" to an asymptotic solution for any lower semi-almost periodic initial function.

    Original languageEnglish
    Pages (from-to)784-807
    Number of pages24
    JournalCommunications in Partial Differential Equations
    Issue number5
    Publication statusPublished - 2008 May


    • Almost periodic functions
    • Hamilton-Jacobi equations
    • Long time behavior
    • Weak KAM theory

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics


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