BOOK REVIEW

摘要

The proposal of the heat equation in 1822 by J.-B. Fourier was a real breakthrough in physical sciences. An essential ingredient in this advance was the introduction of the notion of heat flux. A simple proportionality of this quantity to the gradient of temperature (in modern jargon, an example of constitutive equation) and a rather elementary balance in a small volume took Fourier right to his discovery. Note that this was purely phenomenological and in parallel with the construction of the foundation of continuum mechanics and elasticity by Cauchy. Duhamel was to combine these two apparently non-connected fields of phenomenological physics in the first theory of coupled fields, thermo-elasticity. However, although the dynamical theory of elasticity led to the existence of waves at finite velocity, Fourier's theory produced an instantaneous propagation of heat, and his heat equation became the paragon of so-called parabolic systems. Especially after the formulation of special relativity early in the twentieth century and the requirement that no physical signal should propagate faster than the velocity of light, the validity of physical parabolic field equations was questioned.