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

Ryo Kobayashi, Masakazu Yamamoto, Shuichi Kawashima

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)1097-1121
Number of pages25
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume18
Issue number4
DOIs
Publication statusPublished - 2012 Oct 1
Externally publishedYes

Keywords

  • Decay estimates
  • Drift-diffusion model
  • Stability
  • Weighted energy method

ASJC Scopus subject areas

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

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