Rogolino P, Cimmelli V A
Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d'Alcontres, 31, 98166 Messina, Italy.
Department of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell'Ateneo Lucano, 10, 85100 Potenza, Italy.
Proc Math Phys Eng Sci. 2019 Jan;475(2221):20180482. doi: 10.1098/rspa.2018.0482. Epub 2019 Jan 16.
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.
我们考虑一个源于刚性热导体扩展不可逆热力学的平衡律系统，以及它的微分结果，即通过考虑原始系统的时间和空间导数得到的高阶系统。我们指出了微分结果的一些数学性质，特别关注热扰动以有限速度传播的问题。我们证明，在适当选择初始条件的情况下，微分结果系统的柯西问题的解也是原始系统柯西问题的解。我们通过应用广义科尔曼 - 诺尔程序来研究手头系统的热力学相容性。以广义盖耶 - 克鲁曼斯尔热传输模型为例，我们表明即使状态空间是非局部的，也有可能得到一个双曲型演化方程组。
