KINETIC CONDITION AND THE GIBBS FUNCTION

Abstract

We study the Cauchy problem for a $3\times 3$-system of conservation laws describing the phase transition: $u_t-v_x=0$, $v_t-\sigma(u)_x=0$, $(e+\frac{1}{2}v^2)_t-(\sigma v)_x=0$. 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.