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AIMS Mathematics

2018, Volume 3, Issue 1: 56-65. doi: 10.3934/Math.2018.1.56
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Research article

Large time behavior of a bipolar hydrodynamic model with large data andvacuum

  • Department of Mathematics, LiaoCheng infant normal school, LiaoCheng, 252600, China
  • Received: 06 November 2017 Accepted: 23 January 2018 Published: 01 February 2018

  • MSC : 35L20

  • In this paper, it is considered a hydrodynamic model for the bipolar semiconductor device in the case of a pressure with the exponent γ = 2. The model has a non-flat doping profile and insulating boundary conditions. Firstly, the existence and uniqueness of the corresponding steady solutions which satisfy some bounded estimates are proved. Then, using a technical energy method and an entropy dissipation estimate, we present a framework for the large time behavior of bounded weak entropy solutions with vacuum. It is shown that the weak solutions converge to the stationary solutions in L2 norm with exponential decay rate. No smallness and regularity conditions are assumed.

    Citation: Yunlei Zhan. Large time behavior of a bipolar hydrodynamic model with large data andvacuum[J]. AIMS Mathematics, 2018, 3(1): 56-65. doi: 10.3934/Math.2018.1.56

    Related Papers:

  • In this paper, it is considered a hydrodynamic model for the bipolar semiconductor device in the case of a pressure with the exponent γ = 2. The model has a non-flat doping profile and insulating boundary conditions. Firstly, the existence and uniqueness of the corresponding steady solutions which satisfy some bounded estimates are proved. Then, using a technical energy method and an entropy dissipation estimate, we present a framework for the large time behavior of bounded weak entropy solutions with vacuum. It is shown that the weak solutions converge to the stationary solutions in L2 norm with exponential decay rate. No smallness and regularity conditions are assumed.


    加载中
    [1] L. Yeping, Relaxation limit and initial layer analysis of a bipolar hydrodynamic model for semiconductors, Math. Comput. Model., 50 (2009), 470-480.
    [2] T. Naoki, Existence and uniqueness of stationary solutions to a one-dimensional bipolar hydrodynamic model of semiconductors, Nonlinear Anal-Theor, 73 (2010), 779-787.
    [3] L. Xing and Y. Yan, Large time behavior of solutions to 1-dimensional bipolar quantum hydrodynamic model for semiconductors, Acta Math. Sci., 37 (2017), 806-835.
    [4] Y. Huimin, On the stationary solutions of multi-dimensional bipolar hydrodynamic model of semiconductors, Appl. Math. Lett., 64 (2017), 108-112.
    [5] H. Haifeng, M. Ming and Z. Kaijun, Relaxation limit in bipolar semiconductor hydrodynamic model with non-constant doping profile, J. Math. Anal. Appl., 448 (2017), 1175-1203.
    [6] L. Jing, Y. Huimin, Large time behavior of solutions to a bipolar hydrodynamic model with big Data and vacuum, Nonlinear Anal-Real., 34 (2017), 446-458.
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  • © 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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