Non-classical phase transitions at a sonic point

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.