JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (03): 52-56.doi: 10.6040/j.issn.1671-9352.0.2014.253

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Classical solutions to stationary one-dimensional quantum energy-transport model

DONG Jian-wei, CHENG Shao-hua, WANG Yan-ping   

  1. Department of Mathematics and Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015, Henan, China
  • Received:2014-06-01 Revised:2014-11-07 Online:2015-03-20 Published:2015-03-13

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Abstract: A stationary quantum energy-transport model for semiconductors was studied in a one-dimensional bounded domain. The existence of classical solutions was proved in the case that the heat conductivity depends on the electron density and the electron temperature. Moreover, the uniqueness of the solutions was shown when the lattice temperature was large enough and the current density was relatively small. The proof was based on using an exponential variable transformation, the Leray-Schauder fixed-point theorem and some inequality techniques.

Key words: quantum energy-transport model, existence, uniqueness, stationary solutions

CLC Number: 

  • O175.29
[1] DONG Jianwei, ZHANG Youlin, CHENG Shaohua. Existence of classical solutions to a stationary simplified quantum energy-transport model in 1-dimensional space [J]. Chinese Annals of Mathematics: Series B, 2013, 34(5):691-696.
[2] JUNGEL A, MILISIC J P. A simplified quantum energy-transport model for semiconductors[J].Nonlinear Analysis: Real World Applications, 2011, 12(2): 1033-1046.
[3] CHEN Li, CHEN Xiuqing, JUNGEL A. Semiclassical limit in a simplified quantum energy-transport model for semiconductors [J]. Kinetic and Related Models, 2011, 4(4): 1049-1062.
[4] LI Yong. Global existence and asymptotic behavior for an 1-dimensional compressible energy transport model[J]. Acta Mathematica Sientia, 2009, 29B(5): 1295-1308.
[5] JUNGEL A. Energy transport in semiconductor devices [J]. Math Computer Modelling Dynam Sys, 2010, 16(1): 1-22.
[6] JUNGEL A, PINNAU R, ROHRIG E. Analysis of a bipolar energy-transport model for a metal-oxide-semiconductor diode [J]. J Math Anal Appl, 2011, 378(2): 764-774.
[7] JUNGEL A, KRISTOFEL P. Lyapunove functionals weak sequential stability, and uniqueness analysis for energy-transport systems [J]. Ann Univ Ferrara, 2012, 58(1): 89-100.
[8] JUNGEL A, PINNAU R, ROHRIG E. Existence analysis for a simplified energy-transport model for semiconductors [J]. Math Meth Appl Sci, 2013, 36(13):1701-1712.
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