Logarithmic Sobolev inequalities for bounded domains and applications to drift-diffusion equations

被引：0

作者：

Abdo, Elie ^{[1
]}

Lee, Fizay-Noah ^{[2
]}

机构：

[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

[2] Vanderbilt Univ, Dept Math, Nashville, TN 37235 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2025年 / 288卷 / 01期

关键词：

Logarithmic Sobolev inequalities; Interpolation; Nernst-Planck equations; Long-time dynamics; NERNST-PLANCK;

D O I：

10.1016/j.jfa.2024.110716

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel GagliardoNirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal drift-diffusion models and prove the exponential decay of their solutions to constant steady states. (c) 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

引用

页数：13

共 50 条

[31] Arclength continuation methods and applications to 2D drift-diffusion semiconductor equations
ElBoukili, A
COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING, 1996, 15 (04) : 36 - &
[32] Quantum kinetic and drift-diffusion equations for semiconductor superlattices
Bonilla, LL
Escobedo, R
PROGRESS IN INDUSTRIAL MATHEMATICS AT ECMI 2004, 2006, 8 : 109 - 113
[33] HOLDER CONTINUITY OF SOLUTIONS FOR A CLASS OF DRIFT-DIFFUSION EQUATIONS
Nguyen, Quoc-Hung
Sire, Yannick
Truong, Le Xuan
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2023, 43 (3-4) : 1657 - 1685
[34] AN ADAPTIVE GRID REFINEMENT STRATEGY FOR THE DRIFT-DIFFUSION EQUATIONS
BURGLER, JF
COUGHRAN, WM
FICHTNER, W
IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, 1991, 10 (10) : 1251 - 1258
[35] The bipolar hydrodynamic model for semiconductors and the drift-diffusion equations
Natalini, R
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 198 (01) : 262 - 281
[36] A new derivation of the drift-diffusion equations for electrons and phonons
Rossani, A.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2011, 390 (02) : 223 - 230
[37] Simulation of InSb devices using drift-diffusion equations
Sijercic, E
Mueller, K
Pejcinovic, B
SOLID-STATE ELECTRONICS, 2005, 49 (08) : 1414 - 1421
[38] Arclength continuation methods and applications to 2D drift-diffusion semiconductor equations
ElBoukili, A
Marrocco, A
NUMERICAL METHODS IN ENGINEERING '96, 1996, : 658 - 663
[39] Extremal equilibria for reaction-diffusion equations in bounded domains and applications
Rodriguez-Bernal, Anibal
Vidal-Lopez, Alejandro
JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 244 (12) : 2983 - 3030
[40] Asymptotic analysis of the drift-diffusion equations and Hamilton-Jacobi equations
Montarnal, P
Perthame, B
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1997, 7 (01): : 61 - 80

← 1 2 3 4 5 →