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

Yoshiyuki Kagei

Research output: Contribution to journalArticle

4 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 - Jan 1 2001

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Vlasov-Poisson Equations
Fokker Planck equation
Long-time Asymptotics
Invariant Manifolds
Fokker-Planck Equation
Small Solutions
Sobolev spaces
Variable Transformation
Degenerate Parabolic Equation
Weighted Sobolev Spaces
Similarity Transformation
Large Time Behavior
Unbounded Domain
Parabolic Equation
Cauchy Problem
Nonlinearity

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

Invariant manifolds and long-time asymptotics for the Vlasov-Poisson-Fokker-Planck equation. / Kagei, Yoshiyuki.

In: SIAM Journal on Mathematical Analysis, Vol. 33, No. 2, 01.01.2001, p. 489-507.

Research output: Contribution to journalArticle

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