A note on the long time behavior for the drift-diffusion-Poisson system

被引：24

作者：

Ben Abdallah, N ^{[1
]}

Méhats, F ^{[1
]}

Vauchelet, N ^{[1
]}

机构：

[1] Univ Toulouse 3, UMR 5640, UFR MIG, F-31032 Toulouse 4, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2004年 / 339卷 / 10期

关键词：

D O I：

10.1016/j.crma.2004.09.025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we analyze the long time behavior of a drift-diffusion-Poisson system with a symmetric definite positive diffusion matrix, subject to Dirichlet boundary conditions. This system models the transport of electrons in semiconductor or plasma devices. By using a quadratic relative entropy obtained by keeping the lowest order term of the logarithmic relative entropy, we prove the exponential convergence to the equilibrium. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.

引用

页码：683 / 688

页数：6

共 13 条

[1] Abdallah N., 1994, MATH METHOD APPL SCI, V17, P451
[2] ABDALLAH NB, UNPUB DIFFUSIVE TRAN
[3] On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations
Arnold, A
Markowich, P
Toscani, G
Unterreiter, A
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2001, 26 (1-2) : 43 - 100
[4] On large time asymptotics for drift-diffusion-Poisson systems
Arnold, A
Markowich, P
Toscani, G
[J]. TRANSPORT THEORY AND STATISTICAL PHYSICS, 2000, 29 (3-5): : 571 - 581
[5] Long time behavior of solutions to Nernst-Planck and Debye-Huckel drift-diffusion systems
Biler, P
Dolbeault, J
[J]. ANNALES HENRI POINCARE, 2000, 1 (03): : 461 - 472
[6] Large time asymptotics of nonlinear drift-diffusion systems with Poisson coupling
Biler, P
Dolbeault, J
Markowich, PA
[J]. TRANSPORT THEORY AND STATISTICAL PHYSICS, 2001, 30 (4-6): : 521 - 536
[7] Dolbeault J., 1991, Mathematical Models & Methods in Applied Sciences, V1, P183, DOI 10.1142/S0218202591000113
[8] ON EXISTENCE, UNIQUENESS AND ASYMPTOTIC-BEHAVIOR OF SOLUTIONS OF THE BASIC EQUATIONS FOR CARRIER TRANSPORT IN SEMICONDUCTORS
GAJEWSKI, H
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1985, 65 (02): : 101 - 108
[9] SEMICONDUCTOR EQUATIONS FOR VARIABLE MOBILITIES BASED ON BOLTZMANN STATISTICS OR FERMI-DIRAC STATISTICS
GAJEWSKI, H
GROGER, K
[J]. MATHEMATISCHE NACHRICHTEN, 1989, 140 : 7 - 36
[10] The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model
Gasser, I
Levermore, CD
Markowich, PA
Schmeiser, C
[J]. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2001, 12 : 497 - 512

← 1 2 →