Year: 1998
Author: Gongyan Lei
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 5 : pp. 437–444
Abstract
By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law $\partial_{t} u + \partial_{x} f(u) = 0$, if the flux function $f (u)$ is convex (or concave), then, the physical entropy is $S = -f (u)$; Furthermore, if we assume this result can be generalized to any $f (u)$ with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E-condition can be explained successfully in physics.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1998-JCM-9173
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 5 : pp. 437–444
Published online: 1998-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Conservation laws Entropy Entropy production.