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Non-classical phase transitions at a sonic point. (English) Zbl 1023.35075

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.

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
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