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.


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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