数学与计算机科学 |
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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 |
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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 |
[1] JUNGEL A, MILISIC J P. A simplified quantum energy-transport model for semiconductors[J]. Nonlinear Analysis: Real World Applications, 2011,12(2):1033-1046. [2] CHEN L, CHEN X Q, JUNGEL A. Semiclassical limit in a simplified quantum energy-transport model for semiconductors [J]. Kinetic and Related Models,2011,4(4):1049-1062. [3] DONG J W, ZHANG Y L, CHENG S H. Existence of classical solutions to a stationary simplified quantum energy-transport model in 1-dimensional space[J]. Chinese Annals of Mathematics: Ser B, 2013,34(5):691-696. [4] 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. [5] 董建伟,琚强昌.一个一维半导体简化能量输运模型的稳态解[J].数学年刊:A辑,2014,35(5):613-622. DONG Jianwei, JU Qiangchang. A stationary solution to a 1-dimensional simplified energy-transport modelfor semiconductors[J]. Chinese Annals of Mathematics: SerA,2014,35(5):613-622. [6] JUNGEL A, VIOLET I. The quasi neutral limit in the quantum drift-diffusion equations [J]. Asymptotic Analysis,2007,53(3):139-157. [7] CHEN L, JU Q C. Existence of weak solution and semiclassical limit for quantum drift-diffusion model[J]. Z Angew Math Phys,2007,58(1):1-15. [8] CHEN X Q. The global existence and semiclassical limit of weak solutions to multidi-mensional quantum drift-diffusion model[J]. Advanced Nonlinear Studies,2007,7(1):651-670. [9] CHEN X Q, CHEN L, JIAN H Y. The dirichlet problem of the quantum drift-diffusion model[J]. Nonlinear Analysis,2008,69(9):3084-3092. [10] CHEN X Q, CHEN L. Initial time layer problem for quantum drift-diffusion model[J]. J Math Anal Appl,2008,343(1):64-80. [11] CHEN X Q, CHEN L, JIAN H Y. Existence, semiclassical limit and long-time behavior of weak solution to quantum drift-diffusion model[J]. Nonlinear Analysis: Real World Applications, 2009,10(3):1321-1342. [12] CHEN X Q. The isentropic quantum drift-diffusion model in two or three space dimensions[J]. Z Angew Math Phys,2009,60(3):416-437. [13] NISHIBATA S, SHIGETA N, SUZUKI M. Asymptotic behaviors and classical limits of solutions to a quantum drift-diffusion model for semiconductors [J]. Mathematical Models and Methods in Applied Sciences,2010,20(6):909-936. [14] DONG J W. Classical solutions to the one-dimensional stationary quantum drift-diffusion model[J]. Journal of Mathematical Analysis and Applications,2013,399(2):594-598. [15] 董建伟,张伟.关于一维稳态量子漂移-扩散模型[J].数学进展,2015,44(2):263-270. DONG Jianwei, ZHANG Wei. On the stationary quantum drift-diffusion model in one space dimension [J]. Advances in Mathematics,2015,44(2):263-270. |
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