Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 44, Number 3 (2007), 639-665.
Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors
We study the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for a one-dimensional hydrodynamic model of semiconductors. This problem is considered, in the previous researches  and , under the assumption that a doping profile is flat, which makes the stationary solution also flat. However, this assumption is too narrow to cover the doping profile in actual diode devices. Thus, the main purpose of the present paper is to prove the asymptotic stability of the stationary solution without this assumption on the doping profile. Firstly, we prove the existence of the stationary solution. Secondly, the stability is shown by an elementary energy method, where the equation for an energy form plays an essential role.
Osaka J. Math., Volume 44, Number 3 (2007), 639-665.
First available in Project Euclid: 13 September 2007
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 82D37: Semiconductors 76E99: None of the above, but in this section 76N99: None of the above, but in this section
Secondary: 35L50: Initial-boundary value problems for first-order hyperbolic systems 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]
Nishibata, Shinya; Suzuki, Masahiro. Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors. Osaka J. Math. 44 (2007), no. 3, 639--665. https://projecteuclid.org/euclid.ojm/1189717426