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In this paper the vanishing Debye length limit of the bipolar time-dependent drift-diffusion-Poisson equations modelling insulated semiconductor devices with p-n junctions (i.e., with a fixed bipolar background charge) is studied. For sign-changing and smooth doping profile with 'good' boundary conditions the quasineutral limit (zero-Debye-length limit) is performed rigorously by using the multiple scaling asymptotic expansions of a singular perturbation analysis and the carefully performed classical energy methods. The key point in the proof is to introduce a 'density' transform and two L-weighted Liapunov-type functionals first, and then to establish the entropy production integration inequality, which yields the uniform estimate with respect to the scaled Debye length. The basic point of the idea involved here is to control strong nonlinear oscillation by the interaction between the entropy and the entropy dissipation. (c) 2006 Elsevier Inc. All rights reserved.
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JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN: 0022-0396
Year: 2006
Issue: 2
Volume: 225
Page: 411-439
2 . 4 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
JCR Journal Grade:1
Cited Count:
WoS CC Cited Count: 15
SCOPUS Cited Count: 15
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 5
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