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| Existence of Classical Solutions to a Stationary Simplified Quantum Energy-Transport Model in 1-Dimensional Space |
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Citation： |
Jianwei DONG,Youlin ZHANG,Shaohua CHENG.Existence of Classical Solutions to a Stationary Simplified Quantum Energy-Transport Model in 1-Dimensional Space[J].Chinese Annals of Mathematics B,2013,34(5):691~696 |
| Page view： 1798
Net amount： 1314 |
Authors： |
Jianwei DONG; Youlin ZHANG; Shaohua CHENG; |
Foundation： |
Vital Science Research Foundation of Henan Province Education Department(No. 12A110024). |
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| Abstract： |
The existence of classical solutions to a stationary simplified quantum energytransport
model for semiconductor devices in 1-dimensional space is proved. The model
consists of a nonlinear elliptic third-order equation for the electron density, including a
temperature derivative, an elliptic nonlinear heat equation for the electron temperature,
and the Poisson equation for the electric potential. The proof is based on an exponential
variable transformation and the Leray-Schauder fixed-point theorem. |
Keywords： |
Quantum energy-transport model, Stationary solutions, Existence |
Classification： |
35J40, 35Q40 |
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