Returning to Manne et al. (2000), wherein a class of hyperbolic reaction-diffusion-acoustic models is considered, we show that the inexact transport equation derived by these authors becomes the exact equation for the propagation of second-sound (i.e., thermal waves) in a rigid solid when reformulated under the modified internal energy model, one of several formulations of what has come to be known as hyperbolic heat conduction theory. We then compare/contrast this PDE with/to its exact version, which is based on Cattaneo’s equation for the thermal flux, in the context of a signaling problem involving weak discontinuities of second-sound propagating in a solid rod. Our analysis also reveals a connection between the modified internal energy model and what has been termed “inertial theory”, a competing theory of second-sound in solids, and suggests a generalization of the quantity known as the “thermasy”. We conclude with a discussion on the application of the present findings to a well known, widely applicable, class of nonlinear wave equations.

回到 Manne 等人。（2000），其中考虑了一类双曲反应-扩散-声学模型，我们证明了这些作者导出的不精确的传输方程变成了第二声（即热波）在刚性固体中传播的精确方程。当在修改后的内能模型下重新表述时，这是后来被称为双曲热传导理论的几种公式之一。然后，我们将这个 PDE 与其精确版本进行比较/对比，该版本基于 Cattaneo 的热通量方程，在涉及固体棒中传播的第二声弱不连续性的信号问题的背景下。我们的分析还揭示了修改后的内能模型与所谓的“惯性理论”之间的联系，惯性理论是固体中第二声音的竞争理论，并建议对称为“热热”的数量进行概括。我们最后讨论了将本研究结果应用于众所周知的、广泛适用的一类非线性波动方程。