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

Sablé-Tougeron, Monique

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