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

Naoyuki Ichihara, Hitoshi Ishii

    Research output: Contribution to journalArticle

    19 Citations (Scopus)

    Abstract

    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
    Volume33
    Issue number5
    DOIs
    Publication statusPublished - 2008 May

    Fingerprint

    Hamiltonians
    Asymptotics of Solutions
    Hamilton-Jacobi Equation
    Cauchy Problem
    Asymptotic Solution
    Almost Periodic
    Viscosity Solutions
    Strictly Convex
    Long-time Behavior
    Viscosity
    Converge

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics

    Cite this

    Asymptotic solutions of Hamilton-Jacobi equations with semi-periodic Hamiltonians. / Ichihara, Naoyuki; Ishii, Hitoshi.

    In: Communications in Partial Differential Equations, Vol. 33, No. 5, 05.2008, p. 784-807.

    Research output: Contribution to journalArticle

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