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浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (5): 521-524    DOI: 10.3785/j.issn.1008-9497.2016.05.004
数学与计算机科学     
一维双极量子能量输运稳态模型弱解的存在性
董建伟, 程春蕊, 王艳萍
郑州航空工业管理学院 理学院, 河南 郑州 450015
Existence of weak solutions to a stationary 1-dimensional bipolar quantum energy-transport model
DONG Jianwei, CHENG Chunrui, WANG Yanping
School of Mathematics and Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015, China
 全文: PDF(388 KB)  
摘要： 在一维有界区域上研究一个半导体双极量子能量输运稳态模型.将此模型变形为由2个四阶椭圆方程和1个二阶退化椭圆方程组成的耦合方程组.利用截断方法和Leray-Schauder不动点定理证明了其变形后方程组弱解的存在性.
关键词： 量子能量输运模型;  稳态解;  存在性    
Abstract: A stationary bipolar quantum energy-transport model for semiconductors is studied in a 1-dimensional bounded domain. The model is reformulated as a coupled system consisting of two fourth-order elliptic equations and a second-order degenerate elliptic equation. The existence of weak solutions to the reformulated system is proved using the truncation method and the Leray-Schauder fixed-point theorem.
Key words: quantum energy-transport model    stationary solutions    existence
收稿日期: 2015-10-15 出版日期: 2016-05-01
CLC:  O175.2  
基金资助: 河南省科技厅基础与前沿技术研究计划项目（162300410077）；航空科学基金项目（2013ZD55006）；河南省高等学校青年骨干教师资助计划项目（2013GGJS-142）；郑州航空工业管理学院青年科研基金项目（2013111001，2014113002，2015113001）.
作者简介: 董建伟(1980-),ORCID:http//orcid.org/0000-0003-1131-8244,男,硕士,副教授,主要从事偏微分方程研究,E-mail:dongjianweiccm@163.com.
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引用本文:

董建伟, 程春蕊, 王艳萍. 一维双极量子能量输运稳态模型弱解的存在性[J]. 浙江大学学报（理学版）, 2016, 43(5): 521-524.

DONG Jianwei, CHENG Chunrui, WANG Yanping. Existence of weak solutions to a stationary 1-dimensional bipolar quantum energy-transport model. Journal of ZheJIang University(Science Edition), 2016, 43(5): 521-524.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.05.004    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I5/521

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