Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-28T05:35:15.205Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability and instability of steady-state solutions for a hydrodynamic model of semiconductors

Published online by Cambridge University Press:  14 November 2011

Harumi Hattori
Harumi Hattori
Affiliation:
Department of Mathematics, West Virginia University, Morgantown, WV 26506, U.S.A
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss the stability and instability of steady-state solutions for a hydrodynamic model of semiconductors. We study the case where the doping profile is close to a positive constant and depends on the special variable x. We shall show that a given steady-state solution is asymptotically stable or unstable, depending on whether or not the density of the initial data satisfies P = 0, where P is defined in (3.12).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 4 , 1997 , pp. 781 - 796
Copyright
Copyright © Royal Society of Edinburgh 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Degond, P. and Markovich, P. A.. On a one-dimensional steady-state hydrodynamic model for semiconductors. Appl. Math. Letters 3 (1990), 25–9.CrossRefGoogle Scholar
2Degond, P. and Markovich, P. A.. A steady-state potential flow model for semiconductors. Ann. Mat. puraappl. (IV) (1993), 87–98.CrossRefGoogle Scholar
3Fang, W. and Ito, K.. One-dimensional hydrodynamic model for semiconductors by viscosity method. In Proceedings of the International Conference on Differential Equations, Claremont, CA, June 1994.Google Scholar
4Gamba, I. M.. Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductor. Comm. Partial Differential Equations 17 (1992), 553–77.Google Scholar
5Goodman, J.. Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch. Rational Mech. Anal. 95 (1986), 325–44.CrossRefGoogle Scholar
6Hsiao, L. and Liu, T. P.. Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping. Comm. Math. Phys. 143 (1992), 599–605.CrossRefGoogle Scholar
7Kawashima, S. and Matsumura, A.. Asymptotic stability of traveling wave solution of systems for one-dimensional gas motion. Comm. Math. Phys. 101 (1985), 97–127.CrossRefGoogle Scholar
8Liu, T. P.. Nonlinear stability of shock waves for viscous conservation laws. Mem. Amer. Soc. 328(1985).Google Scholar
9Liu, T. P.. Hyperbolic conservation laws with relaxation. Comm. Math. Phys. 108 (1987), 153–75.CrossRefGoogle Scholar
10Matsumura, A. and Nishida, T.. The initial value problem for the equation of motion of viscous and heat-conductive gases. J. Math. Kyoto Univ. 20(1) (1980), 67–104.Google Scholar