Einstein's evolution equations as a system of balance laws

1989 ◽  
Vol 40 (4) ◽  
pp. 1022-1026 ◽  
Author(s):  
C. Bona ◽  
J. Massó
Keyword(s):  
Evolution Equations ◽  
Balance Laws ◽  
System Of Balance Laws

Lie group analysis and Riemann problems for a 2×2 system of balance laws

2012 ◽  
Vol 51 ◽  
pp. 128-143 ◽  
Author(s):  
Fiammetta Conforto ◽  
Salvatore Iacono ◽  
Francesco Oliveri ◽  
Cecilia Spinelli
Keyword(s):  
Lie Group ◽  
Group Analysis ◽  
Balance Laws ◽  
Lie Group Analysis ◽  
Riemann Problems ◽  
System Of Balance Laws

scholarly journals Asymptotic stability of rarefaction waves for a hyperbolic system of balance laws

2019 ◽  
Vol 12 (4) ◽  
pp. 923-944
Author(s):  
Kenta Nakamura ◽  
◽  
Tohru Nakamura ◽  
Shuichi Kawashima ◽  
◽  
...  
Keyword(s):  
Asymptotic Stability ◽  
Hyperbolic System ◽  
Balance Laws ◽  
Rarefaction Waves ◽  
System Of Balance Laws

scholarly journals Differential consequences of balance laws in extended irreversible thermodynamics of rigid heat conductors

2019 ◽  
Vol 475 (2227) ◽  
pp. 20180482 ◽  
Author(s):  
P. Rogolino ◽  
V. A. Cimmelli
Keyword(s):  
Cauchy Problem ◽  
Evolution Equations ◽  
Transport Model ◽  
Initial Conditions ◽  
Original System ◽  
Irreversible Thermodynamics ◽  
Order System ◽  
Balance Laws ◽  
Extended Irreversible Thermodynamics ◽  
The Cauchy Problem

We consider a system of balance laws arising in extended irreversible thermodynamics of rigid heat conductors, together with its differential conse- quences, namely the higher-order system obtained by taking into account the time and space derivatives of the original system. We point out some mathematical properties of the differential consequences, with particular attention to the problem of the propagation of thermal perturbations with finite speed. We prove that, under an opportune choice of the initial conditions, a solution of the Cauchy problem for the system of differential consequences is also a solution of the Cauchy problem for the original system. We investigate the thermodynamic compatibility of the system at hand by applying a generalized Coleman–Noll procedure. On the example of a generalized Guyer–Krumhansl heat-transport model, we show that it is possible to get a hyperbolic system of evolution equations even when the state space is non-local.

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