Viscous quantum hydrodynamics and parameter‐elliptic systems |
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Authors: | Li Chen Michael Dreher |
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Institution: | 1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China;2. Fachbereich Mathematik und Statistik, Universit?t Konstanz, 78457 Konstanz, Germany |
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Abstract: | The viscous quantum hydrodynamic model derived for semiconductor simulation is studied in this paper. The principal part of the vQHD system constitutes a parameter‐elliptic operator provided that boundary conditions satisfying the Shapiro–Lopatinskii criterion are specified. We classify admissible boundary conditions and show that this principal part generates an analytic semigroup, from which we then obtain the local in time well‐posedness. Furthermore, the exponential stability of zero current and large current steady states is proved, without any kind of subsonic condition. The decay rate is given explicitly. Copyright © 2010 John Wiley & Sons, Ltd. |
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Keywords: | semiconductor model boundary conditions analytic semigroup exponential stability decay rate |
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