Large time asymptotics of nonlinear drift-diffusion systems with poisson coupling

Piotr Biler, Jean Dolbeault, Peter A. Markowich*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


We study the asymptotic behavior as t → + ∞ of a system of densities of charged particles satisfying nonlinear drift-diffusion equations coupled by a damped Poisson equation for the drift-potential. In plasma physics applications the damping is caused by a spatio-temporal rescaling of an "unconfined" problem, which introduces a harmonic external potential of confinement. We present formal calculations (valid for smooth solutions) which extend the results known in the linear diffusion case to nonlinear diffusion of e.g. Fermi-Dirac or fast diffusion/porous media type.

Original languageEnglish (US)
Pages (from-to)521-536
Number of pages16
JournalTransport Theory and Statistical Physics
Issue number4-6
StatePublished - 2001
Externally publishedYes


  • Asymptotic behavior of solutions
  • Fast diffusion
  • Logarithmic sobolev inequalities
  • Nonlinear drift-diffusion systems
  • Porous media

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Transportation
  • General Physics and Astronomy
  • Applied Mathematics


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