Equilibrium and stability properties of detonation waves in the hydrodynamic limit of a kinetic model

A shock wave structure problem, as the one which can be formulated for the planar detonation wave, is analyzed here for a binary mixture of ideal gases undergoing the symmetric reaction A1 + A1 A2 + A2. The problem is studied at the hydrodynamic Euler limit of a kinetic model of the reactive Boltzmann equation. The chemical rate law is deduced in this frame with a second-order reaction rate, in a chemical regime such that the gas flow is not far away from the chemical equilibrium. The caloric and the thermal equations of state for the specific internal energy and temperature are employed to close the system of the balance laws. With respect to other approaches known in the kinetic literature for detonation problems with a reversible reaction, this paper is addressed to improve some aspects of the wave solution. Within the mathematical analysis of the detonation model, the equation of the equilibrium Hugoniot curve of the final states is explicitly derived for the first time and used to define the correct location of the equilibrium Chapman-Jouguet point in the Hugoniot diagram. The parametric space i