Global solution for the mixture of real compressible reacting flows in combustion

The equations for viscous, compressible, heat-conductive, realreactive flows in dynamic combustion are considered, where theequations of state are nonlinear in temperature unlike the lineardependence for perfect gases. The initial-boundary value problemwith Dirichlet-Neumann mixed boundaries in a finite domain isstudied. The existence, uniqueness, and regularity of globalsolutions are established with general large initial data inH¹. It is proved that, although the solutions have largeoscillations, there is no shock wave, turbulence, vacuum, massconcentration, or extremely hot spot developed in any finite time.