Osaka Journal of Mathematics

Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors

Shinya Nishibata and Masahiro Suzuki

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Abstract

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 [2] and [11], 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.

Article information

Source
Osaka J. Math., Volume 44, Number 3 (2007), 639-665.

Dates
First available in Project Euclid: 13 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1189717426

Mathematical Reviews number (MathSciNet)
MR2360944

Zentralblatt MATH identifier
1138.82033

Subjects
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]

Citation

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


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