Vanishing Viscosity Regimes and Nonstandard Shock Relations for Semiconductor Superlattices Models

Thierry Goudon 1, 2, 3 Juan Nieto 4 O. Sanchez 4 Juan Soler 4
1 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
3 SIMPAF - SImulations and Modeling for PArticles and Fluids
Inria Lille - Nord Europe, LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : This 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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Submitted on : Monday, November 18, 2013 - 10:18:48 AM
Last modification on : Friday, April 19, 2019 - 11:24:11 AM

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Thierry Goudon, Juan Nieto, O. Sanchez, Juan Soler. Vanishing Viscosity Regimes and Nonstandard Shock Relations for Semiconductor Superlattices Models. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2011, 71 (1), pp.180--199. ⟨10.1137/090758192⟩. ⟨hal-00905334⟩

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