Breaking symmetry in focusing nonlinear Klein-Gordon equations with potential

    Research output: Contribution to journalArticle

    Abstract

    We study the dynamics for the focusing nonlinear Klein-Gordon equation, utt - Δu + m2u = V (x)|u|p-1u, with positive radial potential V and initial data in the energy space. Under suitable assumption on the potential, we establish the existence and uniqueness of the ground state solution. This enables us to define a threshold size for the initial data that separates global existence and blow-up. An appropriate Gagliardo-Nirenberg inequality gives a critical exponent depending on V. For subcritical exponent and subcritical energy global existence vs blow-up conditions are determined by a comparison between the nonlinear term of the energy solution and the nonlinear term of the ground state energy. For subcritical exponents and critical energy some solutions blow-up, other solutions exist for all time due to the decomposition of the energy space of the initial data into two complementary domains.

    Original languageEnglish
    Pages (from-to)755-788
    Number of pages34
    JournalJournal of Hyperbolic Differential Equations
    Volume15
    Issue number4
    DOIs
    Publication statusPublished - 2018 Dec 1

    Fingerprint

    Nonlinear Klein-Gordon Equation
    Symmetry Breaking
    Energy
    Global Existence
    Blow-up
    Exponent
    Gagliardo-Nirenberg Inequalities
    Ground State Solution
    Blow-up Solution
    Ground State Energy
    Term
    Critical Exponents
    Existence and Uniqueness
    Decompose

    Keywords

    • critical energy
    • global existence/blow up
    • Ground state

    ASJC Scopus subject areas

    • Analysis
    • Mathematics(all)

    Cite this

    Breaking symmetry in focusing nonlinear Klein-Gordon equations with potential. / Gueorguiev, Vladimir Simeonov; Lucente, Sandra.

    In: Journal of Hyperbolic Differential Equations, Vol. 15, No. 4, 01.12.2018, p. 755-788.

    Research output: Contribution to journalArticle

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