Large time behavior in Wasserstein spaces and relative entropy for bipolar drift-diffusion-Poisson models

. We prove asymptotic stability results for nonlinear bipolar drift-diffusion-Poisson Systems arising in semiconductor device modeling and plasma physics in one space dimension. In particular, we prove that, under certain structural assumptions on the external potentials and on the doping profile, a...

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Bibliographic Details
Published inMonatshefte für Mathematik Vol. 154; no. 1; pp. 39 - 50
Main Authors Di Francesco, Marco, Wunsch, Marcus
Format Journal Article
LanguageEnglish
Published Vienna Springer-Verlag 01.05.2008
Subjects
Mathematics
Mathematics and Statistics
2000 Mathematics Subject Classification: 35G25, 45M05 82D37
Key words: Drift-diffusion-Poisson model, Wasserstein distance, finite speed of propagation, entropy dissipation method
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Summary:. We prove asymptotic stability results for nonlinear bipolar drift-diffusion-Poisson Systems arising in semiconductor device modeling and plasma physics in one space dimension. In particular, we prove that, under certain structural assumptions on the external potentials and on the doping profile, all solutions match for large times with respect to all q -Wasserstein distances. We also prove exponential convergence to stationary solutions in relative entropy via the so called entropy dissipation (or Bakry-Émery) method.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-008-0532-6