Asymptotic analysis for a class of infinite systems of first-order PDE: Nonlinear parabolic PDE in the singular limit

Hitoshi Ishii, Kazufumi Shimano

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    We study the asymptotic behavior of solutions of the Cauchy problem for a functional partial differential equation with a small parameter as the parameter tends to zero. We establish a convergence theorem in which the limit problem is identified with the Cauchy problem for a nonlinear parabolic partial differential equation. We also present comparison and existence results for the Cauchy problem for the functional partial differential equation and the limit problem.

    Original languageEnglish
    Pages (from-to)409-438
    Number of pages30
    JournalCommunications in Partial Differential Equations
    Volume28
    Issue number1-2
    Publication statusPublished - 2003

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    Keywords

    • Hamiton-Jacobi equations
    • Infinite system
    • Perturbed test functions
    • Singular limit
    • Viscosity solutions

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics

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