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

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    Keywords

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

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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