Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 22, pp. 1-28.

Title: Non-classical phase transitions at a sonic point

Author: Monique Sable-Tougeron (Univ. de Rennes 1, France)

Abstract: 
 The relevant mathematical features of phase transition for a general
 hyperbolic nonlinear system near a sonic discontinuity are clarified.
 A well-posed Riemann's problem is obtained, including non-classical
 undercompressive shocks, defined by a geometrical kinetic relation.
 A counterpart is the geometrical rejection of some compressive shocks.
 The result is consistent with the structure profiles of the elasticity
 model of Shearer-Yang and the combustion model of Majda.
 
Submitted September 5, 2002. Published March 7, 2003.
Math Subject Classifications: 35L65, 35L67, 74B20, 76L05, 80A32.
Key Words: Hyperbolic; phase transition; Chapman-Jouguet regime; 
           kinetic relation.