Non-local Hamilton-Jacobi equations arising in dislocation dynamics

Hitoshi Ishii, Yutaka Matsumura

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    We investigate a class of non-local Hamilton-Jacobi equations arising in dislocation dynamics. The class of Hamilton-Jacobi equations treated here is a variation of those studied by N. Forcadel, C. Imbert and R. Monneau in [Discrete Contin. Dyn. Syst. 23 (2009) (3), 785-826], and the new feature lies in the singularity at the origin of the kernel functions which describe non-local effects. For the class of Hamilton-Jacobi equations, we establish some stability properties of (viscosity) solutions, comparison theorems between subsolutions and supersolutions and existence theorems of solutions.

    Original languageEnglish
    Pages (from-to)309-350
    Number of pages42
    JournalZeitschrift fur Analysis und ihre Anwendung
    Volume29
    Issue number3
    DOIs
    Publication statusPublished - 2010

    Fingerprint

    Dislocation Dynamics
    Nonlocal Equations
    Hamilton-Jacobi Equation
    Nonlocal Effects
    Supersolution
    Subsolution
    Viscosity Solutions
    Comparison Theorem
    Viscosity
    Kernel Function
    Existence Theorem
    Singularity
    Class

    Keywords

    • Dislocation dynamics
    • Functional differential equations
    • Hamilton-Jacobi equations
    • Viscosity solutions

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Non-local Hamilton-Jacobi equations arising in dislocation dynamics. / Ishii, Hitoshi; Matsumura, Yutaka.

    In: Zeitschrift fur Analysis und ihre Anwendung, Vol. 29, No. 3, 2010, p. 309-350.

    Research output: Contribution to journalArticle

    Ishii, Hitoshi ; Matsumura, Yutaka. / Non-local Hamilton-Jacobi equations arising in dislocation dynamics. In: Zeitschrift fur Analysis und ihre Anwendung. 2010 ; Vol. 29, No. 3. pp. 309-350.
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