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

Ryo Kobayashi; Masakazu Yamamoto; Shuichi Kawashima

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 4, page 1097-1121
- ISSN: 1292-8119

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topKobayashi, Ryo, Yamamoto, Masakazu, and Kawashima, Shuichi. "Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space." ESAIM: Control, Optimisation and Calculus of Variations 18.4 (2012): 1097-1121. <http://eudml.org/doc/272833>.

@article{Kobayashi2012,

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.},

author = {Kobayashi, Ryo, Yamamoto, Masakazu, Kawashima, Shuichi},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {drift-diffusion model; stability; decay estimates; weighted energy method; elliptic-parabolic system; semiconductor device simulation},

language = {eng},

number = {4},

pages = {1097-1121},

publisher = {EDP-Sciences},

title = {Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space},

url = {http://eudml.org/doc/272833},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Kobayashi, Ryo

AU - Yamamoto, Masakazu

AU - Kawashima, Shuichi

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2012

PB - EDP-Sciences

VL - 18

IS - 4

SP - 1097

EP - 1121

AB - 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.

LA - eng

KW - drift-diffusion model; stability; decay estimates; weighted energy method; elliptic-parabolic system; semiconductor device simulation

UR - http://eudml.org/doc/272833

ER -

## References

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