Convergence to global equilibrium for a kinetic fermion model

被引：8

作者：

Neumann, L

Schmeiser, C

机构：

[1] Univ Vienna, Inst Math, A-1090 Vienna, Austria

[2] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

[3] Johann Radon Inst Computat & Appl Math, A-4040 Linz, Austria

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2005年 / 36卷 / 05期

关键词：

kinetic equations; fermions; Fermi-Dirac distribution; semiconductors; H-theorem; relative entropy; entropy dissipation; long-time asymptotics;

D O I：

10.1137/S0036141003436533

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the long-time asymptotics of a kinetic model for fermions in a box with periodic boundary conditions. An entropy dissipation approach is used to prove decay to the global equilibrium for this nonlinear equation, that lacks dissipation in the position variable. We prove convergence at an algebraic rate depending on the smoothness of the solution. The result relies on some initial bounds and a uniform boundedness assumption for spatial derivatives of the solution.

引用

页码：1652 / 1663

页数：12

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