Quasi-neutral limit and the initial layer problem of the electro-diffusion model arising in electro-hydrodynamics

2021 ◽  
Vol 59 ◽  
pp. 103266
Author(s):  
Shu Wang ◽  
Limin Jiang
Keyword(s):  
Diffusion Model ◽  
Initial Layer ◽  
Layer Problem

QUASINEUTRAL LIMIT OF THE DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS WITH GENERAL INITIAL DATA

2003 ◽  
Vol 13 (04) ◽  
pp. 463-470 ◽  
Author(s):  
CHRISTIAN SCHMEISER ◽  
SHU WANG
Keyword(s):  
Initial Data ◽  
Diffusion Model ◽  
Debye Length ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Uniform Estimates ◽  
Initial Layer ◽  
General Initial Data ◽  
Entropy Functionals ◽  
Quasineutral Limit

The limit for vanishing Debye length (charge neutral limit) in a bipolar drift-diffusion model for semiconductors with general initial data allowing the presence of an initial layer is studied. The quasineutral limit (zero-Debye-length limit) is performed rigorously by using two different entropy functionals which yield appropriate uniform estimates. This investigation extends the results of Refs. 7 and 8 for charge neutral initial data where no initial layer occurs.

scholarly journals The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model

2001 ◽  
Vol 12 (4) ◽  
pp. 497-512 ◽  
Author(s):  
INGENUIN GASSER ◽  
C. DAVID LEVERMORE ◽  
PETER A. MARKOWICH ◽  
CHRISTIAN SCHMEISER
Keyword(s):  
Singular Perturbation ◽  
Diffusion Model ◽  
Time Scale ◽  
Initial Time ◽  
Mathematical Tool ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Time Layer ◽  
Quasineutral Limit ◽  
Layer Problem

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.

scholarly journals Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limit

2018 ◽  
Vol 16 (1) ◽  
pp. 1145-1160
Author(s):  
Xiaoting Fan ◽  
Shu Wang ◽  
Wen-Qing Xu ◽  
Mingshuo Liu
Keyword(s):  
Prandtl Number ◽  
Convergence Rates ◽  
Boussinesq System ◽  
Singular Perturbation Theory ◽  
Initial Layer ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Layer Problem

AbstractThe main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Bénard convection with an ill prepared initial data. We use the asymptotic expansion methods of singular perturbation theory and the two-time-scale approach to obtain an exact approximating solution and the convergence rates $O(\varepsilon^{\frac{3}{2}})$ and O(ε2).

A new lithium diffusion model in layered oxides based on asymmetric but reversible transition metal migration

2020 ◽  
Vol 13 (4) ◽  
pp. 1269-1278 ◽  
Author(s):  
Kyojin Ku ◽  
Byunghoon Kim ◽  
Sung-Kyun Jung ◽  
Yue Gong ◽  
Donggun Eum ◽  
...  
Keyword(s):  
Transition Metal ◽  
Diffusion Model ◽  
Layered Oxides ◽  
Layered Oxide ◽  
Reversible Transition ◽  
Lithium Diffusion ◽  
Metal Migration

We propose a new lithium diffusion model involving coupled lithium and transition metal migration, peculiarly occurring in a lithium-rich layered oxide.

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