### AIMS Mathematics

2017, Issue 1: 102-110. doi: 10.3934/Math.2017.1.102
Research article

# Large time behavior framework for the time-increasing weak solutions of bipolar hydrodynamic model of semiconductors

• Received: 05 December 2016 Accepted: 15 January 2017 Published: 09 December 2016
• In this paper, we consider an isentropic Euler-Poisson equations for the bipolar hydrody- namic model of semiconductor devices, which has a non-flat doping profile and insulating boundary conditions. Using a technical energy method and an entropy dissipation estimate, we present a frame- work for the large time behavior of time-increasing weak entropy solutions. It is shown that the weak solutions converge to the stationary solutions in L2 norm with exponential decay rate. No regularity and smallness conditions are assumed.

Citation: Shang Mengmeng. Large time behavior framework for the time-increasing weak solutions of bipolar hydrodynamic model of semiconductors[J]. AIMS Mathematics, 2017, 2(1): 102-110. doi: 10.3934/Math.2017.1.102

### Related Papers:

• In this paper, we consider an isentropic Euler-Poisson equations for the bipolar hydrody- namic model of semiconductor devices, which has a non-flat doping profile and insulating boundary conditions. Using a technical energy method and an entropy dissipation estimate, we present a frame- work for the large time behavior of time-increasing weak entropy solutions. It is shown that the weak solutions converge to the stationary solutions in L2 norm with exponential decay rate. No regularity and smallness conditions are assumed.

 [1] F. Huang, R. Pan, H. Yu, Large time behavior of Euler-Possion system for semiconductor. Science in Chian Series A., 51 (2008), 965-972. [2] L. Hsiao, K.J. Zhang, The relaxation of the hydrodynamic model for semiconducts to the drift- diffusion equations, J. Differential Equations., 165 (2000), 315-354. [3] J. Li, H. Yu, Large time behavior of solutions to a bipolar hydrodynamic model with big data and vacuum, Nonlinear Analysis: Real world applications, 34 (2017), 446-458. [4] P. Marcati, R. Natalini, Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation, Arch. Ration. Mech., 129 (1995), 129-145. [5] H. Yu, On the stationary solutions of multi-dimensional bipolar hydrodynamic model of semicon- ductors, Appl. Math. Lett., 64 (2007), 108-112. [6] H. Yu, Large time behavior of entropy solution to a unipolar hydropynamic model of semiconduc- tors, Commun. Math. Sci., 14 (2016), 69-82. [7] B. Zhang, Convergence of Godunov scheme for a simplified one-dimensional hydrodynamic model for semiconductor devices, Comm. Math. Phys., 157 (1993), 1-22.
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

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