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Asymptotic stability of stationary solutions to thedrift-diffusion model in the whole space
Published online by Cambridge University Press: 16 January 2012
Abstract
We study the initial value problem for the drift-diffusion model arising in semiconductordevice simulation and plasma physics. We show that the corresponding stationary problem inthe whole space ℝn admits a unique stationary solution in ageneral situation. Moreover, it is proved that when n ≥ 3, a uniquesolution to the initial value problem exists globally in time and converges to thecorresponding stationary solution as time tends to infinity, provided that the amplitudeof the stationary solution and the initial perturbation are suitably small. Also, we showthe sharp decay estimate for the perturbation. The stability proof is based on the timeweighted Lp energy method.
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 4 , October 2012 , pp. 1097 - 1121
- Copyright
- © EDP Sciences, SMAI, 2012
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