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A new entropy functional for a scalar conservation law

✍ Scribed by Tai-Ping Liu; Tong Yang

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
82 KB
Volume
52
Category
Article
ISSN
0010-3640

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✦ Synopsis

In this paper we introduce a new entropy functional for a scalar convex conservation law that generalizes the traditional concept of entropy of the second law of thermodynamics. The generalization has two aspects: The new entropy functional is defined not for one but for two solutions. It is defined in terms of the L 1 distance between the two solutions as well as the variations of each separate solution. In addition, it is decreasing in time even when the solutions contain no shocks and is therefore stronger than the traditional entropy even in the case when one of the solutions is zero.

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