Volume 18, Number 4, October-December 2012
|Page(s)||1097 - 1121|
|Published online||16 January 2012|
Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space
Graduate School of Mathematics, Kyushu University,
2 Information Systems Department, Information & Communication Devision, Kyushu Electric Power Co. Inc., 810-8720 Fukuoka, Japan
3 Mathematical Institute, Tohoku University, 980-8578 Sendai, Japan
4 Faculty of Mathematics, Kyushu University, 819-0395 Fukuoka, Japan
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.
Mathematics Subject Classification: 35K45 / 35B35 / 82D10 / 82D37
Key words: Drift-diffusion model / stability / decay estimates / weighted energy method
© EDP Sciences, SMAI, 2012
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