Invariant manifolds and long-time asymptotics for the Vlasov-Poisson-Fokker-Planck equation

Yoshiyuki Kagei

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    We study the large time behavior of small solutions to the Cauchy problem for the Vlasov-Poisson-Fokker-Planck equation, which is a degenerate parabolic equation with nonlocal nonlinearity. We construct finite dimensional invariant manifolds in a neighborhood of the origin in polynomially weighted Sobolev spaces, which enables us to compute systematically the long-time asymptotics for small solutions. To construct invariant manifolds, we make use of the "similarity variables" transformation as in C. E. Wayne's work in 1997, where invariant manifolds for parabolic equations in unbounded domains are constructed.

    Original languageEnglish
    Pages (from-to)489-507
    Number of pages19
    JournalSIAM Journal on Mathematical Analysis
    Volume33
    Issue number2
    DOIs
    Publication statusPublished - 2001

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Computational Mathematics
    • Applied Mathematics

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