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Communications in Partial Differential Equations Volume 24, 1999 - Issue 5-6
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Original Articles

A hierarchy of hydrodynamic models for plasmas zero-relaxation-time limits

Ansgar Jiingel Fachbereich Mathematik, Technische Universitat Berlin, Berlin, D-10623, Germany E-mail: [email protected]
&
Yue-Jun Peng Laboratoire de MathCmatiques AppliquCes, CNRS UMR 6620, Universitk Blaise Pascal, Aubigre cedex, F-63177, France E-mail: [email protected] .fr
Pages 1007-1033 | Published online: 08 May 2007

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Han Sheng & Cunming Liu. (2024) Global error estimates in zero-relaxation limit of Euler–Poisson system for ion dynamics. Applicable Analysis 103:8, pages 1498-1512.
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Jianwei Yang. (2015) Combined relaxation and non-relativistic limit of non-isentropic Euler–Maxwell equations. Applicable Analysis 94:4, pages 747-760.
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Articles from other publishers (57)

Yue-Hong FengHaifeng Hu, Ming Mei, Yue-Jun PengGuo-Jing Zhang. (2024) Relaxation Time Limits of Subsonic Steady States for Hydrodynamic Model of Semiconductors with Sonic or Nonsonic Boundary. SIAM Journal on Mathematical Analysis 56:3, pages 3452-3477.
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Yun-guang Lu. (2024) Global solutions and relaxation limit to the Cauchy problem of a hydrodynamic model for semiconductors. Journal of Differential Equations 393, pages 343-368.
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Yue-Hong Feng, Xin Li, Ming Mei & Shu Wang. (2023) Zero-Relaxation Limits of the Non-Isentropic Euler–Maxwell System for Well/Ill-Prepared Initial Data. Journal of Nonlinear Science 33:5.
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Liang ChenDongfang LiMing Mei & Guojing Zhang. (2023) Quasi-Neutral Limit to Steady-State Hydrodynamic Model of Semiconductors with Degenerate Boundary. SIAM Journal on Mathematical Analysis 55:4, pages 2813-2837.
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Yunguang Lu & Naoki Tsuge. (2023) Uniformly Time-independent L∞ Estimate for a One-dimensional Hydrodynamic Model of Semiconductors. Frontiers of Mathematics 18:2, pages 385-394.
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Silu Yin, Xianting Wang, Yun-guang Lu & Christian Klingenberg. (2022) Global solutions of the Cauchy problem to Euler–Poisson equations of two-carrier types. Applied Mathematics Letters 132, pages 108174.
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Shuang Liu, Yuan Lou & Pengfei Song. (2022) A New Monotonicity for Principal Eigenvalues with Applications to Time-Periodic Patch Models. SIAM Journal on Applied Mathematics 82:2, pages 576-601.
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Yongfu Yang, Qiangchang Ju & Shuang Zhou. (2022) The Global Combined Quasi-Neutral and Zero-Electron-Mass Limit of Non-Isentropic Euler-Poisson Systems. Acta Mathematica Scientia 42:4, pages 1666-1680.
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Yan-bo Hu, C. Klingenberg & Yun-guang Lu. (2020) Zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors. Mathematische Annalen 382:3-4, pages 1031-1046.
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Mingfeng Xie & Weixuan Shi. (2021) Optimal decay estimates for nonisentropic hydrodynamic models of two-carrier plasmas. Journal of Mathematical Analysis and Applications 499:1, pages 125001.
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Changfeng Xue, Christian Klingenberg, Yun-guang Lu & Jin-jun Zhang. (2020) Zero relaxation time limits to isothermal hydrodynamic model for semiconductor. Applied Mathematics Letters 109, pages 106528.
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Yuehong Feng, Xin Li & Shu Wang. (2020) Global zero-relaxation limit of the non-isentropic Euler–Poisson system for ion dynamics. Asymptotic Analysis 120:3-4, pages 301-318.
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Na Chao & Yongfu Yang. (2020) Global relaxation and nonrelativistic limit of nonisentropic Euler‐Maxwell systems. Mathematical Methods in the Applied Sciences 43:9, pages 5692-5707.
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Leilei Tong, Zhong Tan & Qiuju Xu. (2020) Decay estimates of solutions to the bipolar compressible Euler–Poisson system in $$\pmb {\mathbb {R}^3}$$. Zeitschrift für angewandte Mathematik und Physik 71:1.
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Xiaokai Huo, Ansgar Jüngel & Athanasios E Tzavaras. (2019) High-friction limits of Euler flows for multicomponent systems. Nonlinearity 32:8, pages 2875-2913.
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Cunming Liu & Yue‐jun Peng. (2018) Global convergence of the Euler‐Poisson system for ion dynamics. Mathematical Methods in the Applied Sciences 42:4, pages 1236-1248.
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Cunming Liu & Yue-Jun Peng. (2018) Convergence of a non-isentropic Euler–Poisson system for all time. Journal de Mathématiques Pures et Appliquées 119, pages 255-279.
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Victor Wasiolek. (2016) Uniform global existence and convergence of Euler-Maxwell systems with small parameters. Communications on Pure and Applied Analysis 15:6, pages 2007-2021.
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Huimin Yu & Yunlei Zhan. (2016) Large time behavior of solutions to multi-dimensional bipolar hydrodynamic model of semiconductors with vacuum. Journal of Mathematical Analysis and Applications 438:2, pages 856-874.
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Fuzhou Wu. (2016) Initial layer and relaxation limit of non-isentropic compressible Euler equations with damping. Journal of Differential Equations 260:6, pages 5103-5127.
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Jiang Xu & Shuichi Kawashima. (2015) The optimal decay estimates on the framework of Besov spaces for the Euler–Poisson two-fluid system. Mathematical Models and Methods in Applied Sciences 25:10, pages 1813-1844.
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Zhong Tan, Yong Wang & Fanhui Xu. (2015) Large-time behavior of the full compressible Euler-Poisson system without the temperature damping. Discrete and Continuous Dynamical Systems 36:3, pages 1583-1601.
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Yeping Li & Zhiming Zhou. (2015) Relaxation-time limit in the multi-dimensional bipolar nonisentropic Euler–Poisson systems. Journal of Differential Equations 258:10, pages 3546-3566.
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Yong Wang & Zhong Tan. (2015) Stability of steady states of the compressible Euler–Poisson system in . Journal of Mathematical Analysis and Applications 422:2, pages 1058-1071.
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Yue-Jun Peng. (2015) Uniformly Global Smooth Solutions and Convergence of Euler--Poisson Systems with Small Parameters. SIAM Journal on Mathematical Analysis 47:2, pages 1355-1376.
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Yue-Jun Peng & Jiang Xu. (2013) Global well-posedness of the hydrodynamic model for two-carrier plasmas. Journal of Differential Equations 255:10, pages 3447-3471.
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Mohamed‐Lasmer Hajjej & Yue‐Jun Peng. (2012) Initial layers and zero‐relaxation limits of multidimensional Euler–Poisson equations. Mathematical Methods in the Applied Sciences 36:2, pages 182-195.
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Jiang Xu & Qingrong Xu. (2012) Diffusive relaxation limits of compressible Euler–Maxwell equations. Journal of Mathematical Analysis and Applications 386:1, pages 135-148.
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Mohamed-Lasmer Hajjej & Yue-Jun Peng. (2012) Initial layers and zero-relaxation limits of Euler–Maxwell equations. Journal of Differential Equations 252:2, pages 1441-1465.
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Yeping Li & Ting Zhang. (2011) Relaxation-time limit of the multidimensional bipolar hydrodynamic model in Besov space. Journal of Differential Equations 251:11, pages 3143-3162.
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Giuseppe Alì & Li Chen. (2011) The zero-electron-mass limit in the Euler–Poisson system for both well- and ill-prepared initial data. Nonlinearity 24:10, pages 2745-2761.
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Jianwei Yang, Shu Wang, Yong Li & Dang Luo. (2011) The diffusive relaxation limit of non-isentropic Euler–Maxwell equations for plasmas. Journal of Mathematical Analysis and Applications 380:1, pages 343-353.
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Yeping Li. (2011) Relaxation-time limit of the three-dimensional hydrodynamic model with boundary effects. Mathematical Methods in the Applied Sciences 34:10, pages 1202-1210.
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Li Chen, Xiuqing Chen & Chunlei Zhang. (2011) Vanishing electron mass limit in the bipolar Euler–Poisson system. Nonlinear Analysis: Real World Applications 12:2, pages 1002-1012.
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Yue-Jun Peng, Shu Wang & Qilong Gu. (2011) Relaxation Limit and Global Existence of Smooth Solutions of Compressible Euler–Maxwell Equations. SIAM Journal on Mathematical Analysis 43:2, pages 944-970.
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JIANG XU. (2012) ENERGY-TRANSPORT LIMIT OF THE HYDRODYNAMIC MODEL FOR SEMICONDUCTORS. Mathematical Models and Methods in Applied Sciences 20:06, pages 937-954.
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Giuseppe Alì, Li Chen, Ansgar Jüngel & Yue-Jun Peng. (2010) The zero-electron-mass limit in the hydrodynamic model for plasmas. Nonlinear Analysis: Theory, Methods & Applications 72:12, pages 4415-4427.
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Feimin Huang, Tianhong Li & Huimin Yu. (2009) Weak solutions to isothermal hydrodynamic model for semiconductor devices. Journal of Differential Equations 247:11, pages 3070-3099.
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Jiang Xu & Wen-An Yong. (2009) Relaxation-time limits of non-isentropic hydrodynamic models for semiconductors. Journal of Differential Equations 247:6, pages 1777-1795.
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Hsiao Ling & Li Hailiang. (2009) The well-posedness and asymptotics of multi-dimensional quantum hydrodynamics. Acta Mathematica Scientia 29:3, pages 552-568.
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Claire Chainais-Hillairet, Yue-Jue Peng & Ingrid Violet. (2009) Numerical solutions of Euler–Poisson systems for potential flows. Applied Numerical Mathematics 59:2, pages 301-315.
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Jiang Xu. (2009) Relaxation-Time Limit in the Isothermal Hydrodynamic Model for Semiconductors. SIAM Journal on Mathematical Analysis 40:5, pages 1979-1991.
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Ansgar JüngelAnsgar Jüngel. 2009. Transport Equations for Semiconductors. Transport Equations for Semiconductors 1 19 .
Guojing Zhang, Hai-Liang Li & Kaijun Zhang. (2008) Semiclassical and relaxation limits of bipolar quantum hydrodynamic model for semiconductors. Journal of Differential Equations 245:6, pages 1433-1453.
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Qiangchang Ju. (2007) Global smooth solutions to the multidimensional hydrodynamic model for plasmas with insulating boundary conditions. Journal of Mathematical Analysis and Applications 336:2, pages 888-904.
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Ansgar Jüngel, Hai-Liang Li & Akitaka Matsumura. (2006) The relaxation-time limit in the quantum hydrodynamic equations for semiconductors. Journal of Differential Equations 225:2, pages 440-464.
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YUE-JUN PENG & INGRID VIOLET. (2011) ASYMPTOTIC EXPANSIONS IN A STEADY STATE EULER–POISSON SYSTEM AND CONVERGENCE TO INCOMPRESSIBLE EULER EQUATIONS. Mathematical Models and Methods in Applied Sciences 15:05, pages 717-736.
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Wen-An Yong. (2004) Diffusive Relaxation Limit of Multidimensional Isentropic Hydrodynamical Models for Semiconductors. SIAM Journal on Applied Mathematics 64:5, pages 1737-1748.
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Ansgar Jüngel. 2004. Dispersive Transport Equations and Multiscale Models. Dispersive Transport Equations and Multiscale Models 151 166 .
Giuseppe Alı̀ & Ansgar Jüngel. (2003) Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas. Journal of Differential Equations 190:2, pages 663-685.
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Claire Chainais-Hillairet, Jian-Guo Liu & Yue-Jun Peng. (2003) Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. ESAIM: Mathematical Modelling and Numerical Analysis 37:2, pages 319-338.
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Hailiang Li & Peter Markowich. (2001) A review of hydrodynamical models for semiconductors: Asymptotic behavior. Boletim da Sociedade Brasileira de Matem�tica 32:3, pages 321-342.
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Kai-Jun Zhang. (2001) On the Initial-Boundary Value Problem for the Bipolar Hydrodynamic Model for Semiconductors. Journal of Differential Equations 171:2, pages 251-293.
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Yue-Jun Peng. (2002) Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations. ESAIM: Mathematical Modelling and Numerical Analysis 35:2, pages 295-312.
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Ingenuin Gasser & Pierangelo Marcati. (2001) The combined relaxation and vanishing Debye length limit in the hydrodynamic model for semiconductors. Mathematical Methods in the Applied Sciences 24:2, pages 81-92.
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