A convex entropy for a hyperbolic system with relaxation
We explicitly construct a convex entropy function for a hyperbolic system with relaxation. This entropy is defined in the sense of \textit{G.-Q. Chen}, \textit{C. D. Levermore} and \textit{T.-P. Liu} [Commun. Pure Appl. Math. 47, No. 6, 787-830 (1994; Zbl 0806.35112)], which resembles Boltzman's H-theorem for kinetic equations. This construction follows the idea of \textit{I. Suliciu's} [Int. J. Eng. Sci. 28, No. 8, 829-841 (1990; Zbl 0738.73007)] energy function for a rate-type mixed hyperbolic-elliptic system. Such an entropy will be useful in proving the entropy property of the relaxation schemes introduced by the author and \textit{Z. Xin} [Commun. Pure Appl. Math. 48, No. 3, 235-276 (1995; Zbl 0826.65078)] for conservation laws.
scientific article; zbMATH DE number 881703