Hyperbolic principal subsystems: Entropy convexity and subcharacteristic conditions

被引:124
作者
Boillat, G
Ruggeri, T
机构
[1] UNIV BOLOGNA,DEPT MATH,I-40123 BOLOGNA,ITALY
[2] UNIV BOLOGNA,RES CTR APPL MAT,CIRAM,I-40123 BOLOGNA,ITALY
关键词
D O I
10.1007/s002050050030
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a system of N balance laws compatible with an entropy principle and convex entropy density. Using the special symmetric form induced by the main field, we define the concept of principal subsystem associated with the system. We prove that the 2(N) - 2 principal subsystems are also symmetric hyperbolic and satisfy a subentropy law. Moreover we can verify that for each principal subsystem the maximum (minimum) characteristic velocity is not larger (smaller) than the maximum (minimum) characteristic velocity of the full system. These are the subcharacteristic conditions. We present some simple examples in the case of the Euler fluid. Then in the case of dissipative hyperbolic systems we consider an equilibrium principal subsystem and we discuss the consequences in the setting of extended thermodynamics. Finally in the moments approach to the Boltzmann equation we prove, as a consequence of the previous result, that the maximum characteristic velocity evaluated at the equilibrium state does not decrease when the number of moments increases.
引用
收藏
页码:305 / 320
页数:16
相关论文
共 26 条
[1]  
[Anonymous], 1961, SOV MATH DOKL
[2]  
BOILLAT G, 1974, CR ACAD SCI A MATH, V278, P909
[3]  
BOILLAT G, 1979, CR ACAD SCI A MATH, V289, P257
[4]  
Boillat G., 1995, LECT NOTES MATH, V1640, P103
[5]   SPEED OF PROPAGATION OF INFINITESIMAL DISTURBANCES IN A RELATIVISTIC GAS [J].
CERCIGNANI, C .
PHYSICAL REVIEW LETTERS, 1983, 50 (15) :1122-1124
[6]  
Cercignani C., 1988, Applied mathematical sciences
[7]  
CERCIGNANI C, 1985, Z ANGEW MATH PHYS, V36, P699
[8]  
Chapman S., 1961, MATH THEORY NONUNIFO
[9]   HYPERBOLIC CONSERVATION-LAWS WITH STIFF RELAXATION TERMS AND ENTROPY [J].
CHEN, GQ ;
LEVERMORE, CD ;
LIU, TP .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1994, 47 (06) :787-830
[10]  
DAFERMOS C, 1993, 9312 LCDS BROWN U DI