Existence and local uniqueness for the Stokes-Nernst-Planck-drift-diffusion-Poisson system modeling nanopore and nanowire sensors

2019 ◽  
Vol 17 (8) ◽  
pp. 2089-2112
Author(s):  
Leila Taghizadeh ◽  
Clemens Heitzinger
Keyword(s):  
System Modeling ◽  
Poisson System ◽  
Local Uniqueness ◽  
Drift Diffusion ◽  
Nanowire Sensors

An inverse problem for the Vlasov–Poisson system

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Fikret Gölgeleyen ◽  
Masahiro Yamamoto
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Specular Reflection ◽  
Nauk Sssr ◽  
Poisson System ◽  
Local Uniqueness ◽  
Electrical Field ◽  
Stability Theorems ◽  
Akad Nauk Sssr ◽  
Reflection Boundary

AbstractIn this paper, we discuss an inverse problem for the Vlasov–Poisson system. We prove local uniqueness and stability theorems by using the method in Anikonov and Amirov [Dokl. Akad. Nauk SSSR 272 (1983), 1292–1293] under the specular reflection boundary condition and with a prescribed outward electrical field at the boundary.

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.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR A SEMICONDUCTOR DRIFT-DIFFUSION-POISSON MODEL

2008 ◽  
Vol 18 (03) ◽  
pp. 443-487 ◽  
Author(s):  
HAO WU ◽  
PETER A. MARKOWICH ◽  
SONGMU ZHENG
Keyword(s):  
Global Existence ◽  
Existence And Uniqueness ◽  
Poisson Model ◽  
Stationary Problem ◽  
Time Dependent ◽  
Unique Equilibrium ◽  
Poisson System ◽  
Drift Diffusion ◽  
Global Existence And Uniqueness ◽  
Time Dependent Problem

In this paper a time-dependent as well as a stationary drift-diffusion-Poisson system for semiconductors are studied. Global existence and uniqueness of weak solution of the time-dependent problem are proven and we also prove the existence and uniqueness of the steady state. It is shown that as time tends to infinity, the solution of the time-dependent problem will converge to a unique equilibrium. Due to the presence of recombination-generation rate R in our drift-diffusion-Poisson model, the work of this paper in some sense extends the results in the previous literature (on both time-dependent problem and stationary problem).

Global zero-relaxation limit of the non-isentropic Euler–Poisson system for ion dynamics

2020 ◽  
Vol 120 (3-4) ◽  
pp. 301-318
Author(s):  
Yuehong Feng ◽  
Xin Li ◽  
Shu Wang
Keyword(s):  
Relaxation Time ◽  
Energy Estimates ◽  
Ion Dynamics ◽  
Poisson System ◽  
Smooth Solutions ◽  
Drift Diffusion ◽  
Limit System ◽  
Momentum Relaxation ◽  
Global Zero ◽  
Compactness Arguments

This paper is concerned with smooth solutions of the non-isentropic Euler–Poisson system for ion dynamics. The system arises in the modeling of semi-conductor, in which appear one small parameter, the momentum relaxation time. When the initial data are near constant equilibrium states, with the help of uniform energy estimates and compactness arguments, we rigorously prove the convergence of the system for all time, as the relaxation time goes to zero. The limit system is the drift-diffusion system.

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.

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