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一维双极量子流体动力学等温模型稳态解的唯一性 被引量：1

Uniqueness of stationary solutions to 1-d isothermal bipolar quantum hydrodynamic model
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摘要 研究一个耦合的四阶椭圆方程组-δ2/2(uxx+u2x/2)xx+uxx=eu-ev-C(x)+j20(e-2uux)x-j0/τe(e-u)x,-δ2/2(vxx+v2x/2)xx+vxx=eu+ev+C(x)+j21(e-2vvx)x-j1/τi(e-v)x此方程组来源于一维半导体器件中双极量子流体动力学等温稳态模型.在某些条件下利用一些不等式技巧证明了此方程组解的唯一性. The following coupled fourth-order elliptic system is studied： -δ2/2（uxx＋u2x/2）xx＋uxx=eu-ev-C（x）＋j20（e-2uux）x-j0/τe（e-u）x,-δ2/2（vxx＋v2x/2）xx＋vxx=eu＋ev＋C（x）＋j21（e-2vvx）x-j1/τi（e-v）x The system originates from the 1-d stationary isothermal bipolar quantum hydrodynamic model for semiconductor device. The uniqueness of the solutions to the system is proved under some conditions by using some inequality techniques.
作者 董建伟 张又林
机构地区 郑州航空工业管理学院数理系 郑州航空工业管理学院图书馆
出处 《东北师大学报（自然科学版）》 CAS CSCD 北大核心 2015年第3期33-36,共4页 Journal of Northeast Normal University(Natural Science Edition)
基金 河南省科技厅基础与前沿技术研究计划项目(132300410373) 河南省教育厅科学技术研究重点项目(12A110024) 郑州航空工业管理学院青年科研基金资助项目(2013111001 2014113002 2015113001) 航空科学基金资助项目(2013ZD55006) 河南省高等学校青年骨干教师资助计划项目(2013GGJS-142)
关键词 量子流体动力学模型 稳态解 唯一性 quantum hydrodynamic model stationary solutions uniqueness
分类号 O175.29 [理学—基础数学]
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二级参考文献28

  • 1Sun Yuejuan (Dept.of Math.,Shangqiu Normal University,Shangqiu 476000,Henan) Zheng Xiying (Dept.of Math.and Physics,Yellow River Technical College,Zhengzhou 450052).GLOBAL WEAK SOLUTION TO COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY,VACUUM AND GRAVITATIONAL FORCE[J].Annals of Differential Equations,2008,24(1):34-45. 被引量：3
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共引文献4

同被引文献16

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东北师大学报（自然科学版）
2015年 第3期

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