On shock solutions to balance equations for slow and fast chemical reaction

摘要

This paper deals with shock propagation features in a gas mixture undergoing reversible bimolecular reactions, governed by suitable closures at Euler level of Boltzmann-type equations. Slow and fast chemical processes are considered. At macroscopic level, the slow case is described by a set of balance laws, whereas the fast one yields a set of conservation equations. Within the framework of hierarchies of hyperbolic systems, it is possible to prove that the system governing fast reactions is an equilibrium subsystem of the one describing slow reactions, and then to show how the solutions of the slow system converge to those of the fast system, in case of steady shock problems as well as of Riemann problems.