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Kinetic condition and the Gibbs function. (English) Zbl 0951.35078

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.

MSC:

35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
35L67 Shocks and singularities for hyperbolic equations
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