Sablé-Tougeron, Monique Non-classical phase transitions at a sonic point. (English) Zbl 1023.35075 Electron. J. Differ. Equ. 2003, Paper No. 22, 28 p. (2003). This paper deals with phase transition for a nonlinear hyperbolic system near a sonic discontinuity. The analysis is carried out up to the well-posedness of the mixed sonic kinetic Riemann problem; the analysis leads to a geometrical admissibility criterion which explains the rejections of compressible transition shocks as a counterpart of the admissibility of under compressive ones. Finally, the analysis applied to the perturbations of C-J detonations for the complete compressible Euler system. The paper may be of interest to someone working on hyperbolic phase transitions that occur in elasticity and combustion. Reviewer: V.D.Sharma (Mumbai) MSC: 35L65 Hyperbolic conservation laws 35L67 Shocks and singularities for hyperbolic equations 74B20 Nonlinear elasticity 76L05 Shock waves and blast waves in fluid mechanics 80A32 Chemically reacting flows 80A25 Combustion Keywords:hyperbolic; phase transition; Chapman-Jouguet regime; kinetic relation; well-posedness; Riemann problem; compressible Euler system PDF BibTeX XML Cite \textit{M. Sablé-Tougeron}, Electron. J. Differ. Equ. 2003, Paper No. 22, 28 p. (2003; Zbl 1023.35075) Full Text: EuDML EMIS OpenURL