Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On second sound at the critical temperature

Authors: K. Saxton, R. Saxton and W. Kosinski
Journal: Quart. Appl. Math. 57 (1999), 723-740
MSC: Primary 35Q99; Secondary 35L60, 74A15, 80A20
DOI: https://doi.org/10.1090/qam/1724302
MathSciNet review: MR1724302
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Abstract: Based on low-temperature experimental data in solid dielectric crystals, we derive a model of heat conduction for rigid materials using the theory of thermo-dynamic internal state variables. The model is intended to admit wavelike propagation of heat below--and diffusive conduction above--a particular temperature value $ {\vartheta {_\lambda }}$. A rapid decay of the speed of thermal waves occurs just below this temperature, coincident with the conductivity of the material reaching a peak. An analysis of weak and strong discontinuity waves is given in order to exhibit several main features of the proposed model.

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DOI: https://doi.org/10.1090/qam/1724302
Article copyright: © Copyright 1999 American Mathematical Society

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