A new PDE approach to the large time asymptotics of solutions of Hamilton–Jacobi equations

Guy Barles, Hitoshi Ishii, Hiroyoshi Mitake

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    We introduce a new PDE approach to establishing the large time asymptotic behavior of solutions of Hamilton–Jacobi equations, which modifies and simplifies the previous ones (Barles et al. in Arch Ration Mech Anal 204(2):515–558, 2012; Barles and Souganidis in SIAM J Math Anal 31(4):925–939, 2000), under a refined “strict convexity” assumption on the Hamiltonians. Not only such “strict convexity” conditions generalize the corresponding requirements on the Hamiltonians in Barles and Souganidis (SIAM J Math Anal 31(4):925–939, 2000), but also one of the most refined our conditions covers the situation studied in Namah and Roquejoffre (Commun Partial Differ Equ 24(5–6):883–893, 1999).

    Original languageEnglish
    Pages (from-to)363-388
    Number of pages26
    JournalBulletin of Mathematical Sciences
    Volume3
    Issue number3
    DOIs
    Publication statusPublished - 2013 Jan 1

      Fingerprint

    Keywords

    • Asymptotic behavior
    • Hamilton–Jacobi equations
    • PDE approach

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this