From microscopic to macroscopic models: Asymptotic analysis of the Broadwell model toward the wave equation

被引：2
作者：
Bellouquid, A [1 ]
机构：
[1] Politecn Torino, Dipartimento Matemat, I-10129 Turin, Italy
来源：
MATHEMATICAL AND COMPUTER MODELLING | 2002年 / 36卷 / 11-13期
关键词：
discrete Boltzmann equation; kinetic theory; asymptotic theory; wave equation;
D O I：
10.1016/S0895-7177(02)00267-4
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
this paper deals with the asymptotic analysis of the Broadwell model towards the wave equation. Appropriately scaled solutions of the Broadwell model are shown to have fluctuations that locally in time converge weakly to a limit governed by a solution of wave equations provided that the initial fluctuations are smooth. The weak limit becomes strong when the initial fluctuations converge to appropriate initial data. (C) 2002 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码：1169 / 1181
页数：13
相关论文
共 32 条
[11]   High-field limit of the Vlasov-Poisson-Fokker-Planck system: A comparison of different perturbation methods [J].
Bonilla, LL ;
Soler, JS .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2001, 11 (08) :1457-1468
[12]   SHOCK STRUCTURE IN A SIMPLE DISCRETE VELOCITY GAS [J].
BROADWELL, JE .
PHYSICS OF FLUIDS, 1964, 7 (08) :1243-1247
[13]   THE FLUID DYNAMIC LIMIT OF THE NON-LINEAR BOLTZMANN-EQUATION [J].
CAFLISCH, RE .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1980, 33 (05) :651-666
[14]   FLUID-DYNAMICAL LIMIT OF A NON-LINEAR MODEL BOLTZMANN-EQUATION [J].
CAFLISCH, RE ;
PAPANICOLAOU, GC .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1979, 32 (05) :589-616
[15]   INCOMPRESSIBLE NAVIER-STOKES AND EULER LIMITS OF THE BOLTZMANN-EQUATION [J].
DEMASI, A ;
ESPOSITO, R ;
LEBOWITZ, JL .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (08) :1189-1214
[16]   LIMIT THEOREMS FOR MODEL BOLTZMANN EQUATIONS WITH SEVERAL CONSERVED QUANTITIES [J].
ELLIS, RS ;
PINSKY, MA .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1973, 23 (04) :287-307
[17]   ASYMPTOTIC EQUIVALENCE OF LINEAR NAVIER-STOKES AND HEAT EQUATIONS IN ONE DIMENSION [J].
ELLIS, RS ;
PINSKY, MA .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1975, 17 (02) :406-420
[18]  
GATIGNOL R, 1975, LECT NOTES PHYSICS, V36
[19]  
GOLSE F, 2001, STOKESFOURIER ACOUST, P1
[20]   Generalized discrete velocity models [J].
Görsch, D .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (01) :49-75
1234