New mathematical models of combustion process (thermal theory combustion process and vibration combustion) are developed based on thermodynamic analysis. The global inhomogeneity of the system can be characterized as an inhomogeneous distribution of the enthalpy over the flow (mixture). In this case, the combustion process in the phase space \( (\varrho , P, T, n, S, E) \) , the increment of the enthalpy is not a total differential, but it is a total differential on the local equilibrium manifold. These two assertions allow one to single out in the phase space the state equations for the pressure and entropy. The resulting pressure and entropy close the classical model of hydrodynamics and kinetics, which describes the laminar stage of the combustion process. Our numerical experiments shows that the two combustion regimes (deflagration and detonation) depend on the structure of the standard value of the chemical potential. In addition, if the passive component velocity is controlled at the inlet, then, depending on the structure, there appear high-frequency acoustic oscillations described by Raushenbakh. Moreover, for critical values of the chemical potential, such oscillations cause a blow-up.
