ISSN:
1432-0959
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract A set of symmetric hyberbolic field equations, describing heat conduction in dielectric solids at low temperatures, is studied with respect to the propagation of temperature shock waves. The field equations have been derived from the Boltzmann-Peierls equation and include the phenomenon of second sound, a special form of wavelike energy transport occuring in some crystals in a temperature range close to absolute zero. Two physical criteria, an entropy shock condition and the Lax condition, which is based on a causality argument, are applied to study the existence of so called “hot” and “cold” shocks. These are characterized by a temperature rise or fall across the shock respectively, and it turns out that the only possible solution to the problem is a “hot” shock, predicted by either one of the criteria. In the recent literature, however, a similar case was treated revealing a partial contradiction between the two criteria. Regarding the fact that there exists a proof of equivalence for small shocks, we were thus led to investigate this equivalence in the general case, which is illustrated by means of a simple example.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01126385
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