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 journal › Article

    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

    Fingerprint

    Singular Limit
    Asymptotic analysis
    Nonlinear Parabolic Equations
    Infinite Systems
    Asymptotic Analysis
    Partial differential equations
    Partial Functional Differential Equation
    Cauchy Problem
    First-order
    Parabolic Partial Differential Equations
    Comparison Result
    Asymptotic Behavior of Solutions
    Nonlinear Partial Differential Equations
    Convergence Theorem
    Small Parameter
    Existence Results
    Tend
    Zero
    Class

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics

    Cite this

    Asymptotic analysis for a class of infinite systems of first-order PDE : Nonlinear parabolic PDE in the singular limit. / Ishii, Hitoshi; Shimano, Kazufumi.

    In: Communications in Partial Differential Equations, Vol. 28, No. 1-2, 2003, p. 409-438.

    Research output: Contribution to journal › Article

    Ishii, H & Shimano, K 2003, 'Asymptotic analysis for a class of infinite systems of first-order PDE: Nonlinear parabolic PDE in the singular limit', Communications in Partial Differential Equations, vol. 28, no. 1-2, pp. 409-438.
    Ishii H, Shimano K. Asymptotic analysis for a class of infinite systems of first-order PDE: Nonlinear parabolic PDE in the singular limit. Communications in Partial Differential Equations. 2003;28(1-2):409-438.
    Ishii, Hitoshi ; Shimano, Kazufumi. / Asymptotic analysis for a class of infinite systems of first-order PDE : Nonlinear parabolic PDE in the singular limit. In: Communications in Partial Differential Equations. 2003 ; Vol. 28, No. 1-2. pp. 409-438.
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