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December  2009, 25(4): 1319-1332. doi: 10.3934/dcds.2009.25.1319

Zero-relaxation limit of non-isentropic hydrodynamic models for semiconductors

Jiang Xu 1, and  Wen-An Yong 2,

1. 

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2. 

Zhou Pei-Yuan Center for Appl. Math., Tsinghua University, Beijing 100084, China

Received  November 2008 Revised  June 2009 Published  September 2009

This paper deals with non-isentropic hydrodynamic models for semiconductors with short momentum and energy relaxation times. With the help of the Maxwell iteration, we construct a new approximation and show that periodic initial-value problems of certain scaled non-isentropic hydrodynamic models have unique smooth solutions in a time interval independent of the two relaxation times. Furthermore, it is proved that as the two relaxation times both tend to zero, the smooth solutions converge to solutions of the corresponding semilinear drift-diffusion models.
Keywords: relaxation limit, continuation principle, Non-isentropic hydrodynamic model, energy estimates., Maxwell iteration.
Mathematics Subject Classification: Primary: 35B25, 35L45; Secondary: 35M2.
Citation: Jiang Xu, Wen-An Yong. Zero-relaxation limit of non-isentropic hydrodynamic models for semiconductors. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1319-1332. doi: 10.3934/dcds.2009.25.1319
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