A new entropy functional for a scalar conservation law |
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| Authors: | Tai-Ping Liu Tong Yang |
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| Affiliation: | 1. Stanford University, Department of Mathematics, Stanford, CA 94305-2125;2. City University of Hong Kong, Department of Mathematics, 83 Tat Chee Avenue, Kowloon Tong, Kowloon, Hong Kong |
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| 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 L1 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. |
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