DIFFUSION LIMIT AND THE OPTIMAL CONVERGENCE RATE OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM

被引：1

作者：

Zhong, Mingying ^{[1
]}

机构：

[1] Guangxi Univ, Coll Math & Informat Sci, Nanning, Peoples R China

来源：

基金：

中国国家自然科学基金;

关键词：

Vlasov-Poisson-Fokker-Planck system; spectral analysis; diffusion limit; convergence rate; GLOBAL WEAK SOLUTIONS; HIGH-FIELD LIMIT; ASYMPTOTIC-BEHAVIOR; CLASSICAL-SOLUTIONS; TIME BEHAVIOR; EXISTENCE;

D O I：

10.3934/krm.2021041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we study the diffusion limit of the classical solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system with initial data near a global Maxwellian. We prove the convergence and establish the optimal convergence rate of the global strong solution to the VPFP system towards the solution to the drift-diffusion-Poisson system based on the spectral analysis with precise estimation on the initial layer.

引用

页码：1 / 26

页数：26

共 35 条

[1]

[Anonymous], 1995, Differential Integ. Equations

[2] On large time asymptotics for drift-diffusion-Poisson systems [J].

Arnold, A ;

Markowich, P ;

Toscani, G .

TRANSPORT THEORY AND STATISTICAL PHYSICS, 2000, 29 (3-5) :571-581

[3]

Bardos C., 1991, Mathematical Models & Methods in Applied Sciences, V1, P235, DOI 10.1142/S0218202591000137

[4] EXISTENCE AND ASYMPTOTICS OF SOLUTIONS FOR A PARABOLIC-ELLIPTIC SYSTEM WITH NONLINEAR NO-FLUX BOUNDARY-CONDITIONS [J].

BILER, P .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1992, 19 (12) :1121-1136

[5] THE DEBYE SYSTEM - EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTIONS [J].

BILER, P ;

HEBISCH, W ;

NADZIEJA, T .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 23 (09) :1189-1209

[6] Long time behavior of solutions to Nernst-Planck and Debye-Huckel drift-diffusion systems [J].

Biler, P ;

Dolbeault, J .

ANNALES HENRI POINCARE, 2000, 1 (03) :461-472

[7] Asymptotic behavior of an initial-boundary value problem for the Vlasov-Poisson-Fokker-Planck system [J].

Bonilla, LL ;

Carrillo, JA ;

Soler, J .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1997, 57 (05) :1343-1372

[8] EXISTENCE AND UNIQUENESS OF A GLOBAL SMOOTH SOLUTION FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM IN 3 DIMENSIONS [J].

BOUCHUT, F .

JOURNAL OF FUNCTIONAL ANALYSIS, 1993, 111 (01) :239-258

[9] SMOOTHING EFFECT FOR THE NONLINEAR VLASOV-POISSON-FOKKER-PLANCK SYSTEM [J].

BOUCHUT, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 122 (02) :225-238

[10] Asymptotic behaviour and self-similarity for the three dimensional Vlasov-Poisson-Fokker-Planck system [J].

Carrillo, JA ;

Soler, J ;

Vazquez, JL .

JOURNAL OF FUNCTIONAL ANALYSIS, 1996, 141 (01) :99-132

← 1 2 3 4 →