The stationary solution of a one-dimensional bipolar quantum hydrodynamic model |
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Authors: | Jing Hu Yeping Li Jie Liao |
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Institution: | 1. School of Science, East China University of Science and Technology, Shanghai, 200237, PR China;2. School of Science, Nantong University, Nantong, 226019, PR China |
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Abstract: | In this paper, we consider the existence and uniqueness of stationary solution to the bipolar quantum hydrodynamic model in one dimensional space with general non-constant doping profile. The existence of the stationary solution is proved by Leray-Schauder fixed-point theorem and a crucial truncation technique is used to derive the positive upper and lower bounds of the stationary solution. The uniqueness of the stationary solution is shown by a delicate energy estimate. |
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Keywords: | Bipolar quantum hydrodynamic model Stationary solution Existence Uniqueness |
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