AIMS Mathematics, 2017, 2(1): 102-110. doi: 10.3934/Math.2017.1.102

Research article

Export file:

Format

• RIS(for EndNote,Reference Manager,ProCite)
• BibTex
• Text

Content

• Citation Only
• Citation and Abstract

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

Department of Mathematics, Shandong Normal University, Jinan, 250014, China

## Abstract    Full Text(HTML)    Figure/Table

In this paper, we consider an isentropic Euler-Poisson equations for the bipolar hydrodynamic 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 framework for the large time behavior of time-increasing weak entropy solutions. It is shown that the weak solutions converge to the stationary solutions in $L^2$ norm with exponential decay rate. No regularity and smallness conditions are assumed.
Figure/Table
Supplementary
Article Metrics

# References

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. Di erential 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-di usion 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.