Electron. J. Diff. Eqns., Vol. 2003(2003), No. 22, pp. 1-28.

Non-classical phase transitions at a sonic point

Monique Sable-Tougeron

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.

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Monique Sable-Tougeron
I.R.M.A.R., Universite de Rennes 1
Campus de Beaulieu
F-35042 Rennes Cedex, France
email: sable@maths.univ-rennes1.fr

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