On large time asymptotics for drift-diffusion-Poisson systems

Anton Arnold*, Peter Markowich, Giuseppe Toscani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


In this paper we analyze the convergence rate of solutions of certain drift-diffusion-Poisson systems to their unique steady state. These bi-polar equations model the transport of two populations of charged particles and have applications for semiconductor devices and plasmas. When prescribing a confinement potential for the particles we prove exponential convergence to the equilibrium. Without confinement the solution decays with an algebraic rate towards a self-similar state. The analysis is based on a relative entropy type functional and it uses logarithmic Sobolev inequalities.

Original languageEnglish (US)
Pages (from-to)571-581
Number of pages11
JournalTransport Theory and Statistical Physics
Issue number3-5
StatePublished - 2000
Externally publishedYes

ASJC Scopus subject areas

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


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