On large time asymptotics for drift-diffusion-Poisson systems

被引：45

作者：

Arnold, A

Markowich, P

Toscani, G

机构：

[1] Tech Univ Berlin, Fachbereich Math, D-10623 Berlin, Germany

[2] Univ Linz, Inst Anal & Numer, A-4040 Linz, Austria

[3] Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy

来源：

TRANSPORT THEORY AND STATISTICAL PHYSICS | 2000年 / 29卷 / 3-5期

关键词：

D O I：

10.1080/00411450008205893

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we analyze the convergence rate of solutions of certain drift-diffusion-Poisson systems to their unique steady state. These hi-polar equations model the transport of two populations of charged particles and have applications for semiconductor devices and plasmas. When prescribing a confinement potential for the particles we prove exponential convergence to the equilibrium. Without confinement the solution decays with an algebraic rate towards a self-similar state. The analysis is based on a relative entropy type functional and it uses logarithmic Sobolev inequalities.

引用

页码：571 / 581

页数：11

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