| The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model |
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| 作者姓名： | Xiuqing CHEN~* Li CHEN~ |
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| 作者单位： | Xiuqing CHEN~* Li CHEN~(**) Huaiyu JIAN~(**) *School of Sciences，Beijing University of Posts and Telecommunications，Beijing 100876，China. **Department of Mathematical Sciences，Tsinghua University，Beijing 100084，China. |
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| 摘 要： | The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.
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| 关 键 词： | 弱解 两极量子转移模型 长期性 存在性 |
| 收稿时间： | 26 December 2006 |
The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model* |
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| Xiuqing CHEN* Li CHEN.The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model[J].Chinese Annals of Mathematics,Series B,2007,28(6):651-664. |
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| Authors: | Xiuqing Chen Li Chen Huaiyu Jian |
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| Institution: | 1. School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China
2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
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| Abstract: | The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity. |
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| Keywords: | Quantum drift-diffusion Weak solution Long-time behavior |
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