Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions

Hitoshi Ishii

    Research output: Contribution to journalArticle

    12 Citations (Scopus)

    Abstract

    We study the long-time asymptotic behavior of solutions u of the Hamilton-Jacobi equation ut(x, t) + H(x, Du(x, t)) = 0 in Ω × (0, ∞), where Ω is a bounded open subset of ℝn, with Hamiltonian H = H(x, p) being convex and coercive in p, and establish the uniform convergence of u to an asymptotic solution as t → ∞.

    Original languageEnglish
    Pages (from-to)189-209
    Number of pages21
    JournalCalculus of Variations and Partial Differential Equations
    Volume42
    Issue number1
    DOIs
    Publication statusPublished - 2011 Sep

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    Hamiltonians
    Long-time Asymptotics
    Asymptotic Solution
    Hamilton-Jacobi Equation
    Long-time Behavior
    Asymptotic Behavior of Solutions
    Uniform convergence
    Set theory
    Boundary conditions
    Subset

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions. / Ishii, Hitoshi.

    In: Calculus of Variations and Partial Differential Equations, Vol. 42, No. 1, 09.2011, p. 189-209.

    Research output: Contribution to journalArticle

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