Steady Hydrodynamic Model of Semiconductors with Sonic Boundary: (II) Supersonic Doping Profile
Steady Hydrodynamic Model of Semiconductors with Sonic Boundary: (II) Supersonic Doping Profile
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具有声边界的半导体稳态流体动力学模型：(II) 超声掺杂分布
DOI：
10.1137/17m1129477
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发表时间：
2016-10
影响因子：
2
通讯作者：
Zhang Kaijun
中科院分区：
文献类型：
--
作者：
Li Jingyu;Mei Ming;Zhang Guojing;Zhang Kaijun
In this paper, we study the well-posedness/ill-posedness and regularity of stationary solutions to the hydrodynamic model of semiconductors represented by Euler-Poisson equations with sonic boundary. When the doping profile is subsonic, we prove that, the steady-state equations with sonic boundary possess a unique interior subsonic solution, and at least one interior supersonic solution, and if the relaxation time is large and the doping profile is a small perturbation of constant, then the equations admit infinitely many transonic shock solutions, while, if the relaxation time is small enough and the doping profile is a subsonic constant, then the equations admits infinitely many $C^1$ smooth transonic solutions, and no transonic shock solution exists. When the doping profile is supersonic, we show that the system does not hold any subsonic solution, furthermore, the system doesn't admit any supersonic solution or any transonic solution if such a supersonic doping profile is small or the relaxation time is small, but it has at least one supersonic solution and infinitely many transonic solutions if the supersonic doping profile is close to the sonic line and the relaxation time is large. The interior subsonic/supersonic solutions all are global $C^{\frac{1}{2}}$ H\"older-continuous, and the exponent $\frac{1}{2}$ is optimal. The non-existence of any type solutions in the case of small doping profile or small relaxation time indicates that the semiconductor effect for the system is remarkable and cannot be ignored. The proof for the existence of subsonic/supersonic solutions is the technical compactness analysis combining the energy method and the phase-plane analysis, while the approach for the existence of multiple transonic solutions is artfully constructed. The results obtained significantly improve and develop the existing studies.
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DOI：
10.1016/j.aml.2006.01.015
发表时间：
2006-12
期刊：
Appl. Math. Lett.
影响因子：
--
作者：
Yue-Jun Peng;Ingrid Violet
通讯作者：
Yue-Jun Peng;Ingrid Violet
DOI：
10.1007/978-3-7091-6961-2
发表时间：
1990
期刊：
--
影响因子：
--
作者：
P. Markowich;C. Ringhofer;C. Schmeiser
通讯作者：
P. Markowich;C. Ringhofer;C. Schmeiser
DOI：
--
发表时间：
2007
期刊：
--
影响因子：
--
作者：
Gui-Qiang G. Chen;C. Dafermos;M. Slemrod;Dehua Wang
通讯作者：
Gui-Qiang G. Chen;C. Dafermos;M. Slemrod;Dehua Wang
影响因子：
1
作者：
T. Luo;Z. Xin
通讯作者：
T. Luo;Z. Xin
影响因子：
2.4
作者：
Chunpeng Wang
通讯作者：
Chunpeng Wang