An asymptotic analysis for Hamilton-Jacobi equations with large Hamiltonian drift terms

Taiga Kumagai

    Research output: Contribution to journalArticle

    Abstract

    We investigate the asymptotic behavior of solutions of Hamilton-Jacobi equations with large Hamiltonian drift terms in an open subset of the two-dimensional Euclidean space. The drift is given by ϵ - 1 ( H x 2 , - H x 1 ) -1(H2,-Hx1) of a Hamiltonian H, with ϵ > 0 >0 . We establish the convergence, as ϵ → 0 + to 0+ , of solutions of the Hamilton-Jacobi equations and identify the limit of the solutions as the solution of systems of ordinary differential equations on a graph. This result generalizes the previous one obtained by the author to the case where the Hamiltonian H admits a degenerate critical point and, as a consequence, the graph may have more than four segments at a node.

    Original languageEnglish
    JournalUnknown Journal
    DOIs
    Publication statusAccepted/In press - 2017 Nov 14

    Fingerprint

    Hamilton-Jacobi equation
    Hamiltonians
    Asymptotic analysis
    Hamilton-Jacobi Equation
    Asymptotic Analysis
    Term
    Euclidean geometry
    Asymptotic Behavior of Solutions
    Graph in graph theory
    Set theory
    System of Ordinary Differential Equations
    Ordinary differential equations
    set theory
    Euclidean space
    Critical point
    critical point
    differential equations
    Generalise
    Subset
    Vertex of a graph

    Keywords

    • graphs
    • Hamilton-Jacobi equations
    • large drift
    • Singular perturbation

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    An asymptotic analysis for Hamilton-Jacobi equations with large Hamiltonian drift terms. / Kumagai, Taiga.

    In: Unknown Journal, 14.11.2017.

    Research output: Contribution to journalArticle

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