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A new entropy functional for a scalar conservation law
Author(s) -
Liu TaiPing,
Yang Tong
Publication year - 1999
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199911)52:11<1427::aid-cpa2>3.0.co;2-r
Subject(s) - mathematics , conservation law , entropy (arrow of time) , second law of thermodynamics , regular polygon , statistical physics , mathematical economics , mathematical analysis , thermodynamics , physics , geometry
Abstract 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. © 1999 John Wiley & Sons, Inc.