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Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors

Published online by Cambridge University Press:  12 July 2007

Hailiang Li
Affiliation:
SISSA, Via Beirut 2-4, Trieste 34014, Italy and Institute of Mathematics, Academia Sinica, Beijing 100080, People's Republic of China
Peter Markowich
Affiliation:
Institute of Mathematics, University of Vienna, Boltzmanngasse 9, 1090 Vienna, Austria
Ming Mei
Affiliation:
Institute of Applied Mathematics and Numerical Analysis, Vienna University of Technology, A-1040 Vienna, Austria

Abstract

Degond and Markowich discussed the existence and uniqueness of a steady-state solution in the subsonic case for the one-dimensional hydrodynamic model of semiconductors. In the present paper, we reconsider the existence and uniqueness of a globally smooth subsonic steady-state solution, and prove its stability for small perturbation. The proof method we adopt in this paper is based on elementary energy estimates.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2002

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