scholarly journals The relaxation limit of bipolar fluid models

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nuno J. Alves ◽  
Athanasios E. Tzavaras
Keyword(s):  
Weak Solution ◽  
Smooth Solution ◽  
Vacuum Solution ◽  
Relative Energy ◽  
Diffusion System ◽  
Fluid Models ◽  
Energy Identity ◽  
Poisson System ◽  
Drift Diffusion ◽  
Friction Regime

<p style='text-indent:20px;'>This work establishes the relaxation limit from the bipolar Euler-Poisson system to the bipolar drift-diffusion system, for data so that the latter has a smooth solution. A relative energy identity is developed for the bipolar fluid models, and it is used to show that a dissipative weak solution of the bipolar Euler-Poisson system converges in the high-friction regime to a strong and bounded away from vacuum solution of the bipolar drift-diffusion system.</p>

ON THE 3-D BIPOLAR ISENTROPIC EULER–POISSON MODEL FOR SEMICONDUCTORS AND THE DRIFT-DIFFUSION LIMIT

2000 ◽  
Vol 10 (03) ◽  
pp. 351-360 ◽  
Author(s):  
CORRADO LATTANZIO
Keyword(s):  
Relaxation Time ◽  
Weak Solutions ◽  
Hydrodynamic Model ◽  
Poisson Model ◽  
Diffusion System ◽  
Diffusion Limit ◽  
Poisson System ◽  
Drift Diffusion ◽  
Bipolar Hydrodynamic Model

The aim of this paper is the study of the relaxation limit of the 3-D bipolar hydrodynamic model for semiconductors. We prove the convergence for the weak solutions to the bipolar Euler–Poisson system towards the solutions to the bipolar drifthyphen;diffusion system, as the relaxation time tends to zero.

scholarly journals On a Drift–Diffusion System for Semiconductor Devices

2016 ◽  
Vol 17 (12) ◽  
pp. 3473-3498 ◽  
Author(s):  
Rafael Granero-Belinchón
Keyword(s):  
Semiconductor Devices ◽  
Diffusion System ◽  
Drift Diffusion

A NUMERICAL ANALYSIS OF A REACTION–DIFFUSION SYSTEM MODELING THE DYNAMICS OF GROWTH TUMORS

2010 ◽  
Vol 20 (05) ◽  
pp. 731-756 ◽  
Author(s):  
VERÓNICA ANAYA ◽  
MOSTAFA BENDAHMANE ◽  
MAURICIO SEPÚLVEDA
Keyword(s):  
Weak Solution ◽  
Numerical Analysis ◽  
Numerical Scheme ◽  
System Modeling ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Existence Of Weak Solutions ◽  
Early Tumor ◽  
Volume Method

We consider a reaction–diffusion system of 2 × 2 equations modeling the spread of early tumor cells. The existence of weak solutions is ensured by a classical argument of Faedo–Galerkin method. Then, we present a numerical scheme for this model based on a finite volume method. We establish the existence of discrete solutions to this scheme, and we show that it converges to a weak solution. Finally, some numerical simulations are reported with pattern formation examples.

scholarly journals Generalized Logarithmic Hardy–Littlewood–Sobolev Inequality

2019 ◽  
Author(s):  
Jean Dolbeault ◽  
Xingyu Li
Keyword(s):  
Sobolev Inequality ◽  
Nonlinear Diffusion ◽  
Opposite Sign ◽  
Entropy Method ◽  
Nonlinear Diffusion Equation ◽  
Sobolev Inequalities ◽  
Poisson System ◽  
Drift Diffusion ◽  
Reverse Inequality ◽  
Logarithmic Growth

Abstract This paper is devoted to logarithmic Hardy–Littlewood–Sobolev inequalities in the 2D Euclidean space, in the presence of an external potential with logarithmic growth. The coupling with the potential introduces a new parameter, with two regimes. The attractive regime reflects the standard logarithmic Hardy–Littlewood–Sobolev inequality. The 2nd regime corresponds to a reverse inequality, with the opposite sign in the convolution term, which allows us to bound the free energy of a drift–diffusion–Poisson system from below. Our method is based on an extension of an entropy method proposed by E. Carlen, J. Carrillo, and M. Loss, and on a nonlinear diffusion equation.

scholarly journals Uniform-in-time bounds for approximate solutions of the drift–diffusion system

2019 ◽  
Vol 141 (4) ◽  
pp. 881-916
Author(s):  
M. Bessemoulin-Chatard ◽  
C. Chainais-Hillairet
Keyword(s):  
Approximate Solutions ◽  
Diffusion System ◽  
Drift Diffusion ◽  
Time Bounds

scholarly journals Bridging kinetic plasma descriptions and single-fluid models

2020 ◽  
Vol 86 (5) ◽  
Author(s):  
A. Crestetto ◽  
F. Deluzet ◽  
D. Doyen
Keyword(s):  
Numerical Methods ◽  
Low Frequency ◽  
Model Coupling ◽  
Fluid Models ◽  
Maxwell System ◽  
Poisson System ◽  
Microscopic Description ◽  
Frequency Model ◽  
Multi Scale

The purpose of this paper is to bridge kinetic plasma descriptions and low-frequency single-fluid models. More specifically, the asymptotics leading to magnetohydrodynamic regimes starting from the Vlasov–Maxwell system are investigated. The analogy with the derivation, from the Vlasov–Poisson system, of a fluid representation for ions coupled to the Boltzmann relation for electrons is also outlined. The aim is to identify asymptotic parameters explaining the transitions from one microscopic description to a macroscopic low-frequency model. These investigations provide groundwork for the derivation of multi-scale numerical methods, model coupling or physics-based preconditioning.

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