Vanishing Viscosity Regimes and Nonstandard Shock Relations for Semiconductor Superlattices Models

Abstract

International audienceThis paper is concerned with the analysis of asymptotic problems from discrete drift-diffusion models describing charge transport in semiconductor superlattices. The regimes we are interested in lead to balance laws. However, the nonconservative structure of the discrete system might produce defect measure terms in the limit process. These defect terms, concentrated on the shock discontinuities, can be related to nonstandard jump relations (in contrast with the usual Rankine-Hugoniot law) when considering discontinuous solutions and wave fronts

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“…On the other hand, in the hyperbolic (high¯eld) limit the in°uence of the di®usion terms is of lower (or equal) order of magnitude compared with other convective or interaction terms and the aim is to derive hyperbolic macroscopic models. 21,36,37 Therefore, di®erent macroscopic models are obtained in agreement with di®erent scaling assumptions, see Ref. 52.…”