Abstract.
The aim of this paper is the rigorous derivation of a non-linear drift-diffusion model from the Boltzmann equation in a semiconductor device. Collisions are taken into account through the non-linear Pauli operator, without assuming any relation concerning the cross-section (such as the so-called detailed balance principle). The proof of the convergence relies on a formal Hilbert expansion and the estimation of the remainder. The same program is applied to the derivation of a non-linear SHE (Spherical Harmonics Expansion) model, when elastic collisions are considered, and is rigorously carried through in the case of zero electric field.
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(Received 5 October 2000; in revised form 3 September 2001)
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Mellet, A. Diffusion Limit of a Non-Linear Kinetic Model without the Detailed Balance Principle. Mh Math 134, 305–329 (2002). https://doi.org/10.1007/s605-002-8265-1
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DOI: https://doi.org/10.1007/s605-002-8265-1