Geodesic
Supplementary balance laws for Cattaneo heat propagation
Communications in Mathematics, Tome 21 (2013) no. 2, pp. 161-171
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In this work we determine for the Cattaneo heat propagation system all the supplementary balance laws (shortly SBL) of the same order (zero) as the system itself and extract the constitutive relations (expression for the internal energy) dictated by the Entropy Principle. The space of all supplementary balance laws (having the functional dimension 8) contains four original balance laws and their deformations depending on 4 functions of temperature ($\lambda^0(\vartheta), K^A(\vartheta), A=1,2,3 $). The requirements of the II law of thermodynamics leads to the exclusion of three functional degrees ($K^A=0, A=1,2,3$) and to further restriction to the form of internal energy. In its final formulation, entropy balance represents the deformation of the energy balance law by the functional parameter $\lambda^{0}(\vartheta)$.
In this work we determine for the Cattaneo heat propagation system all the supplementary balance laws (shortly SBL) of the same order (zero) as the system itself and extract the constitutive relations (expression for the internal energy) dictated by the Entropy Principle. The space of all supplementary balance laws (having the functional dimension 8) contains four original balance laws and their deformations depending on 4 functions of temperature ($\lambda^0(\vartheta), K^A(\vartheta), A=1,2,3 $). The requirements of the II law of thermodynamics leads to the exclusion of three functional degrees ($K^A=0, A=1,2,3$) and to further restriction to the form of internal energy. In its final formulation, entropy balance represents the deformation of the energy balance law by the functional parameter $\lambda^{0}(\vartheta)$.
Classification : 35Q79, 70S10
Keywords: Cattaneo balance equations; conservation laws; entropy 
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Preston, Serge. Supplementary balance laws for Cattaneo heat propagation. Communications in Mathematics, Tome 21 (2013) no. 2, pp. 161-171. http://geodesic.mathdoc.fr/item/COMIM_2013_21_2_a4/

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