Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians

Naoyuki Ichihara, Hitoshi Ishii*

*この研究の対応する著者

    研究成果査読

    25 被引用数 (Scopus)

    抄録

    We investigate the long-time behavior of viscosity solutions of Hamilton-Jacobi equations in ℝn with convex and coercive Hamiltonians and give three general criteria for the convergence of solutions to asymptotic solutions as time goes to infinity. We apply the criteria to obtain more specific sufficient conditions for the convergence to asymptotic solutions and then examine them with examples. We take a dynamical approach, based on tools from weak KAM theory such as extremal curves, Aubry sets and representation formulas for solutions, for these investigations.

    本文言語English
    ページ(範囲)383-419
    ページ数37
    ジャーナルArchive for Rational Mechanics and Analysis
    194
    2
    DOI
    出版ステータスPublished - 2009 9

    ASJC Scopus subject areas

    • 分析
    • 機械工学
    • 数学(その他)

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