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《清华大学学报(自然科学版)(英文版)》 2008-04
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Dirichlet-Neumann Problem for Unipolar Isentropic Quantum Drift-Diffusion Model

CHEN Li **, CHEN Xiuqing Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China  
This paper studies the existence, semiclassical limit, and long-time behavior of weak solutions to the unipolar isentropic quantum drift-diffusion model, a fourth order parabolic system. Semi-discretization in time and entropy estimates give the global existence and semiclassical limit of nonnegative weak solutions to the one-dimensional model with a nonnegative large initial value and a Dirichlet-Neumann boundary con- dition. Furthermore, the weak solutions are proven to exponentially approach constant steady state as time increases to infinity.
【Fund】: the National Natural Science Foundation of China(No. 10401019)
【CateGory Index】: O471.1
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Chinese Journal Full-text Database 5 Hits
1 LIANG Bo(School of Mathematics and Physics,Dalian Jiaotong University,Dalian 116028,China);Exponential Decay of Solutions for Quantum Drift-Diffuse Model[J];Journal of Dalian Jiaotong University;2009-04
2 Y. Zhang C. Zheng Y Liu L. Shao · C. Gou School of Mechanical and Vehicular Engineering,Beijing Institute of Technology, 100081 Beijing, China Y.Liu School of Mechanical-Electronic and Automobile Engineering, Beijing University of Civil Engineering and Architecture,100044 Beijing, China;Two exact solutions of the DPL non-Fourier heat conduction equation with special conditions[J];力学学报(英文版);2009-02
3 CHEN Xiuqing (School of Sciences,Beijing Univ.of Posts and Telecommunications,Beijing,100876,P.R.China);The Regularity of Global Weak Solution for a Fourth-order Parabolic Equation[J];Advances in Mathematics;2009-03
4 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.;The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model[J];数学年刊B辑(英文版);2007-06
5 Li CHEN~* Qiangchang JU~(**) *Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China. **Institute of Applied Pnysics and Computational Mathematics,P.O.Box 8009-28,Beijing 100088,China.;The Semiclassical Limit in the Quantum Drift-Diffusion Equations with Isentropic Pressure[J];数学年刊B辑(英文版);2008-04
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