Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space

Ryo Kobayashi, Masakazu Yamamoto, Shuichi Kawashima

研究成果: Contribution to journalArticle

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We study the initial value problem for the drift-diffusion model arising in semiconductor device simulation and plasma physics. We show that the corresponding stationary problem in the whole space ℝn admits a unique stationary solution in a general situation. Moreover, it is proved that when n ≥ 3, a unique solution to the initial value problem exists globally in time and converges to the corresponding stationary solution as time tends to infinity, provided that the amplitude of the stationary solution and the initial perturbation are suitably small. Also, we show the sharp decay estimate for the perturbation. The stability proof is based on the time weighted Lp energy method.

元の言語英語
ページ(範囲)1097-1121
ページ数25
ジャーナルESAIM - Control, Optimisation and Calculus of Variations
18
発行部数4
DOI
出版物ステータス出版済み - 10 2012

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

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