A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton-Jacobi equations

Hitoshi Ishii

    Research output: Chapter in Book/Report/Conference proceedingChapter

    11 Citations (Scopus)

    Abstract

    We present an introduction to the theory of viscosity solutions of first-order partial differential equations and a review on the optimal control/dynamical approach to the large time behavior of solutions of Hamilton-Jacobi equations, with the Neumann boundary condition. This article also includes some of basics of mathematical analysis related to the optimal control/dynamical approach for easy accessibility to the topics.

    Original languageEnglish
    Title of host publicationLecture Notes in Mathematics
    Pages111-249
    Number of pages139
    Volume2074
    DOIs
    Publication statusPublished - 2013

    Publication series

    NameLecture Notes in Mathematics
    Volume2074
    ISSN (Print)00758434

    Fingerprint

    Large Time Behavior
    Hamilton-Jacobi Equation
    Viscosity Solutions
    Behavior of Solutions
    Optimal Control
    First order differential equation
    Neumann Boundary Conditions
    Accessibility
    Mathematical Analysis
    Partial differential equation
    Review

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Ishii, H. (2013). A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton-Jacobi equations. In Lecture Notes in Mathematics (Vol. 2074, pp. 111-249). (Lecture Notes in Mathematics; Vol. 2074). https://doi.org/10.1007/978-3-642-36433-4-3

    A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton-Jacobi equations. / Ishii, Hitoshi.

    Lecture Notes in Mathematics. Vol. 2074 2013. p. 111-249 (Lecture Notes in Mathematics; Vol. 2074).

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Ishii, H 2013, A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton-Jacobi equations. in Lecture Notes in Mathematics. vol. 2074, Lecture Notes in Mathematics, vol. 2074, pp. 111-249. https://doi.org/10.1007/978-3-642-36433-4-3
    Ishii H. A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton-Jacobi equations. In Lecture Notes in Mathematics. Vol. 2074. 2013. p. 111-249. (Lecture Notes in Mathematics). https://doi.org/10.1007/978-3-642-36433-4-3
    Ishii, Hitoshi. / A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton-Jacobi equations. Lecture Notes in Mathematics. Vol. 2074 2013. pp. 111-249 (Lecture Notes in Mathematics).
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