Asakura, Fumioki Kinetic condition and the Gibbs function. (English) Zbl 0951.35078 Taiwanese J. Math. 4, No. 1, 105-117 (2000). Summary: We study the Cauchy problem for a \(3\times 3\)-system of conservation laws describing the phase transition: \(u_t- v_x= 0\), \(v_t- \sigma(u)_x= 0\), \(\left(e+{1\over 2} v^2\right)_t- (\sigma v)_x= 0\). A phase boundary is said to be admissible if it satisfies the Abeyaratne-Knowles kinetic condition. We give a physical account of the kinetic condition by means of the Gibbs function. We also obtain a useful description of the entropy function using the Gibbs function. Cited in 2 Documents MSC: 35L65 Hyperbolic conservation laws 35L45 Initial value problems for first-order hyperbolic systems 35L67 Shocks and singularities for hyperbolic equations Keywords:phase transition; Abeyaratne-Knowles kinetic condition; entropy function PDFBibTeX XMLCite \textit{F. Asakura}, Taiwanese J. Math. 4, No. 1, 105--117 (2000; Zbl 0951.35078) Full Text: DOI