magazinelogo

Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 ISSN Print: 2576-0645 CODEN: JAMCEZ
Frequency: quarterly Email: jamc@hillpublisher.com
Total View: 2482876 Downloads: 444611 Citations: 362 (From Dimensions)
ArticleOpen Access http://dx.doi.org/10.26855/jamc.2022.03.005

Large Time Behavior of Entropy Solutions to Two-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

Lili Chen

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

*Corresponding author: Lili Chen

Published: February 22, 2022

Abstract

This paper mainly studies the large time behavior of two-dimensional isothermal spherically symmetric compressible Euler-Poisson equations with variable coefficient damping in a bounded region. This equation and its variants have been used to describe the dynamic behavior of many important physical flows including the propagation of electrons in submicron semiconductor devices, the biological transport of ions for channel proteins, the motion of stars in the theory of general relativity and so on. This paper mainly proves that the weak solution converges exponentially to the unique stationary solution in time. The main methods are entropy estimation and energy method. Here, the key step is to construct an appropriate entropy estimation to cooperate with the energy method to obtain that when t→∞, the spherically symmetric weak solution of the isothermal spherically symmetric Euler-Poisson equations with variable coefficient damping converges to the unique smooth solution of the corresponding stationary equations at an exponential rate under the condition that the corresponding initial values are satisfied.

Keyword

Euler-Poisson equations, Damping, Large time behavior, Weak entropy solution

References

[1] F. M. Huang, R. H. Pan, H. M. Yu. (2008). Large time behavior of Euler-Poisson system for semiconductor. Sci. China Ser. A., 51, 965-972.

[2] H. M. Yu. (2010). Large time behavior of Euler-Poisson equations for isothermal fluids with spherical symmetry. J. Math. Anal. Appl., 363, 302-309.

[3] H. M. Yu. (2015). Large time behavior of entropy solutions to a unipolar hydrodynamic model of Semiconductors. Comm. Math. Sci., 14, 69-82.

[4] L. Hsiao, T. Yang. (2001). Asymptotics of initial boundary value problems for hydrodynamic and driftdiffusion models for semiconductors. J. Differ. Equ., 170, 472-493. 

[5] F. M. Huang, M. Mei, Y. Wang, H. M. Yu. (2011). Asymptotic convergence to planar stationary waves for multi-dimensional unipolar hydrodynamic model of semiconductors. J. Differ. E-qu., 251, 1305-1331.

[6] G. Q. Chen, T. H. Li. (2003). Global entropy solutions in linfinity to the Euler equations and Euler-Poisson equations for isothermal fluids with spherical symmetry. Methods Appl. Anal., 10, 215-244.

[7] Y. Guo. (1998). Smooth irrotational flows in the large to the Euler-Poisson system in R3+1. Commun. Math. Phys., 195, 249-265.

[8] F. M. Huang, Z. Wang. (2003). Convergence of viscosity solutions for isentropic gas dynamics. SIAMJ. Math. Anal., 34, 595-610.

[9] F. M. Huang, T. H. Li, H. M. Yu, D. F. Yuan. (2018). Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices. Z. Angew. Math. Phys., 69, 69.

[10] Y.G. Lu. (2011). Resonance for the isothermal system of isentropic gas dynamics. Proc. Amer. Math.Soc., 139, 2821-2826.

[11] Y. G. Lu. (2002). Hyperbolic conservation laws and the compensated compactness method. CRC Press.

[12] H. M. Yu, Y. L. Zhan. (2016). Large time behavior of solutions to multi-dimensional bipolar hydrodynamic model of semiconductors with vacuum. J. Math. Anal. Appl., 438, 856-874.

Copyright

© 2022 by the author(s).
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) license, which permits non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited and is not modified or adapted.
https://creativecommons.org/licenses/by-nc-nd/4.0/

How to cite this paper

Large Time Behavior of Entropy Solutions to Two-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

How to cite this paper: Lili Chen. (2022) Large Time Behavior of Entropy Solutions to Two-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping. Journal of Applied Mathematics and Computation6(1), 24-29.

DOI: http://dx.doi.org/10.26855/jamc.2022.03.005