Christov C I, Jordan P M
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504, USA.
Phys Rev Lett. 2005 Apr 22;94(15):154301. doi: 10.1103/PhysRevLett.94.154301.
In this Letter, we revisit the Maxwell-Cattaneo law of finite-speed heat conduction. We point out that the usual form of this law, which involves a partial time derivative, leads to a paradoxical result if the body is in motion. We then show that by using the material derivative of the thermal flux, in lieu of the local one, the paradox is completely resolved. Specifically, that using the material derivative yields a constitutive relation that is Galilean invariant. Finally, we show that under this invariant reformulation, the system of governing equations, while still hyperbolic, cannot be reduced to a single transport equation in the multidimensional case.
在这封信中，我们重新审视了有限速度热传导的麦克斯韦 - 卡塔尼奥定律。我们指出，该定律的通常形式涉及偏时间导数，如果物体处于运动状态，会导致一个矛盾的结果。然后我们表明，通过使用热通量的物质导数代替局部导数，这个矛盾可以完全解决。具体来说，使用物质导数会产生一个伽利略不变的本构关系。最后，我们表明在这种不变的重新表述下，控制方程组虽然仍然是双曲型的，但在多维情况下不能简化为单个输运方程。
