Finite Time Extinction for Nonlinear Schrödinger Equation in 1D and 2D

Rémi Carles, Tohru Ozawa

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    We consider a nonlinear Schrödinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra superlinear damping to prevent finite time blow up, we show that the presence of a sublinear damping always leads to finite time extinction of the solution in 1D, and that the same phenomenon is present in the case of small mass initial data in 2D.

    Original languageEnglish
    Pages (from-to)897-917
    Number of pages21
    JournalCommunications in Partial Differential Equations
    Volume40
    Issue number5
    DOIs
    Publication statusPublished - 2015 Jan 1

    Fingerprint

    Extinction Time
    Nonlinear equations
    Damping
    Nonlinear Equations
    Finite Time Blow-up
    Compact Manifold
    One Dimension
    Two Dimensions
    Harmonic
    Nonlinearity

    Keywords

    • Asymptotic behavior
    • Finite time extinction
    • Nonlinear damping
    • Nonlinear Schrödinger equation

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Finite Time Extinction for Nonlinear Schrödinger Equation in 1D and 2D. / Carles, Rémi; Ozawa, Tohru.

    In: Communications in Partial Differential Equations, Vol. 40, No. 5, 01.01.2015, p. 897-917.

    Research output: Contribution to journalArticle

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