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Hydrodynamic Equations

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Transport Equations for Semiconductors

Part of the book series: Lecture Notes in Physics ((LNP,volume 773))

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In Sect. 2.1, we have considered two different time scalings. In the diffusion scaling, assumed in Chaps. 5, 6, 7, and 8, the typical time is of the order of the time between two consecutive collisions divided by the square of the Knudsen number α2, which is supposed to be small compared to 1. In this chapter, we consider a shorter time scale. More precisely, we suppose that the typical time is of the order of the time between two scattering events divided by α. We show that with this scaling hydrodynamic equations can be derived. In contrast to the models of the previous chapters, hydrodynamic models are mathematically not of parabolic but of hyperbolic type.

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  1. TU Wien Inst. Analysis und Scientific Computing, Wiedner Hauptstr. 8-10, 1040 Wien, Austria

    Ansgar Jüngel (Prof. Dr)

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  1. Ansgar Jüngel
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Jüngel, A. (2009). Hydrodynamic Equations. In: Transport Equations for Semiconductors. Lecture Notes in Physics, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89526-8_9

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  • DOI: https://doi.org/10.1007/978-3-540-89526-8_9

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