# American Institute of Mathematical Sciences

April  1999, 5(2): 449-455. doi: 10.3934/dcds.1999.5.449

## The relaxation to the drift-diffusion system for the 3-$D$ isentropic Euler-Poisson model for semiconductors

 1 Dipartimento di Matematica Pura ed Applicata, Università degli Studi di L'Aquila, Via Vetoio, loc. Coppito - 67010 L'Aquila, Italy, Italy

Revised  September 1998 Published  January 1999

In this paper we are concerned with the study of the relaxation limit of the 3-$D$ hydrodynamic model for semiconductors. We prove the convergence of the weak solutions to the Euler-Poisson system toward the solutions to the drift-diffusion system, as the relaxation time tends to zero.
Citation: Corrado Lattanzio, Pierangelo Marcati. The relaxation to the drift-diffusion system for the 3-$D$ isentropic Euler-Poisson model for semiconductors. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 449-455. doi: 10.3934/dcds.1999.5.449
 [1] Xueke Pu. Quasineutral limit of the Euler-Poisson system under strong magnetic fields. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 2095-2111. doi: 10.3934/dcdss.2016086 [2] Shu Wang, Chundi Liu. Boundary Layer Problem and Quasineutral Limit of Compressible Euler-Poisson System. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2177-2199. doi: 10.3934/cpaa.2017108 [3] Jianwei Yang, Dongling Li, Xiao Yang. On the quasineutral limit for the compressible Euler-Poisson equations. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022020 [4] Yeping Li. Existence and some limit analysis of stationary solutions for a multi-dimensional bipolar Euler-Poisson system. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 345-360. doi: 10.3934/dcdsb.2011.16.345 [5] Qiangchang Ju, Hailiang Li, Yong Li, Song Jiang. Quasi-neutral limit of the two-fluid Euler-Poisson system. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1577-1590. doi: 10.3934/cpaa.2010.9.1577 [6] Jiang Xu, Ting Zhang. Zero-electron-mass limit of Euler-Poisson equations. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4743-4768. doi: 10.3934/dcds.2013.33.4743 [7] Myoungjean Bae, Yong Park. Radial transonic shock solutions of Euler-Poisson system in convergent nozzles. Discrete and Continuous Dynamical Systems - S, 2018, 11 (5) : 773-791. doi: 10.3934/dcdss.2018049 [8] Léo Bois, Emmanuel Franck, Laurent Navoret, Vincent Vigon. A neural network closure for the Euler-Poisson system based on kinetic simulations. Kinetic and Related Models, 2022, 15 (1) : 49-89. doi: 10.3934/krm.2021044 [9] A. Alexandrou Himonas, Gerard Misiołek, Feride Tiǧlay. On unique continuation for the modified Euler-Poisson equations. Discrete and Continuous Dynamical Systems, 2007, 19 (3) : 515-529. doi: 10.3934/dcds.2007.19.515 [10] Dongfen Bian, Huimin Liu, Xueke Pu. Modulation approximation for the quantum Euler-Poisson equation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4375-4405. doi: 10.3934/dcdsb.2020292 [11] Ming Mei, Yong Wang. Stability of stationary waves for full Euler-Poisson system in multi-dimensional space. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1775-1807. doi: 10.3934/cpaa.2012.11.1775 [12] Zhong Tan, Yong Wang, Fanhui Xu. Large-time behavior of the full compressible Euler-Poisson system without the temperature damping. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1583-1601. doi: 10.3934/dcds.2016.36.1583 [13] Myoungjean Bae, Hyangdong Park. Three-dimensional supersonic flows of Euler-Poisson system for potential flow. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2421-2440. doi: 10.3934/cpaa.2021079 [14] Hai-Liang Li, Tong Yang, Mingying Zhong. Diffusion limit of the Vlasov-Poisson-Boltzmann system. Kinetic and Related Models, 2021, 14 (2) : 211-255. doi: 10.3934/krm.2021003 [15] Yongcai Geng. Singularity formation for relativistic Euler and Euler-Poisson equations with repulsive force. Communications on Pure and Applied Analysis, 2015, 14 (2) : 549-564. doi: 10.3934/cpaa.2015.14.549 [16] Yeping Li, Jie Liao. Stability and $L^{p}$ convergence rates of planar diffusion waves for three-dimensional bipolar Euler-Poisson systems. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1281-1302. doi: 10.3934/cpaa.2019062 [17] Qiwei Wu. Large-time behavior of solutions to the bipolar quantum Euler-Poisson system with critical time-dependent over-damping. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022008 [18] Hong Cai, Zhong Tan. Stability of stationary solutions to the compressible bipolar Euler-Poisson equations. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 4677-4696. doi: 10.3934/dcds.2017201 [19] La-Su Mai, Kaijun Zhang. Asymptotic stability of steady state solutions for the relativistic Euler-Poisson equations. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 981-1004. doi: 10.3934/dcds.2016.36.981 [20] Manwai Yuen. Cylindrical blowup solutions to the isothermal Euler-Poisson equations. Conference Publications, 2011, 2011 (Special) : 1448-1456. doi: 10.3934/proc.2011.2011.1448

2021 Impact Factor: 1.588