Gasser, Ingenuin; Levermore, C. David; Markowich, Peter A.; Schmeiser, Christian The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model. (English) Zbl 1018.82024 Eur. J. Appl. Math. 12, No. 4, 497-512 (2001). Summary: The classical time-dependent drift-diffusion model for semiconductors is considered for small scaled Debye length (which is a singular perturbation parameter). The corresponding limit is carried out on both the dielectric relaxation time scale and the diffusion time scale. The latter is a quasineutral limit, and the former can be interpreted as an initial time layer problem. The main mathematical tool for the analytically rigorous singular perturbation theory of this paper is the (physical) entropy of the system. Cited in 1 ReviewCited in 33 Documents MSC: 82D37 Statistical mechanics of semiconductors Keywords:time-dependent drift-diffusion model; semiconductors; small scaled Debye length; singular perturbation; dielectric relaxation time scale; diffusion time scale; quasineutral limit; entropy PDFBibTeX XMLCite \textit{I. Gasser} et al., Eur. J. Appl. Math. 12, No. 4, 497--512 (2001; Zbl 1018.82024) Full Text: DOI