High energy rotation type solutions of the forced pendulum equation

Patricio Felmer, André De Laire, Salomé Martínez, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    Abstract

    In this article we study the existence and asymptotic profiles of high-energy rotation type solutions of the singularly perturbed forced pendulum equation ε2u'ε+sin uε= ε in (-L, L). We prove that the asymptotic profile of these solutions is described in terms of an energy function which satisfy an integro-differential equation. Also we show that given a suitable energy function E satisfying the integro-differential equation, a family of solutions of the pendulum equation above exists having E as the asymptotic profile, when ε → 0.

    Original languageEnglish
    Pages (from-to)1473-1499
    Number of pages27
    JournalNonlinearity
    Volume26
    Issue number5
    DOIs
    Publication statusPublished - 2013 May

    Fingerprint

    Asymptotic Profile
    Integrodifferential equations
    pendulums
    Pendulum
    Pendulums
    High Energy
    Energy Function
    Integro-differential Equation
    differential equations
    profiles
    Singularly Perturbed
    energy

    ASJC Scopus subject areas

    • Applied Mathematics
    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    High energy rotation type solutions of the forced pendulum equation. / Felmer, Patricio; Laire, André De; Martínez, Salomé; Tanaka, Kazunaga.

    In: Nonlinearity, Vol. 26, No. 5, 05.2013, p. 1473-1499.

    Research output: Contribution to journalArticle

    Felmer, Patricio ; Laire, André De ; Martínez, Salomé ; Tanaka, Kazunaga. / High energy rotation type solutions of the forced pendulum equation. In: Nonlinearity. 2013 ; Vol. 26, No. 5. pp. 1473-1499.
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