On the large-time behavior of 1D radiative and reactive viscous flows for higher-order kinetics

We consider the system of quasilinear equations describing 1D radiative and reactive viscous flows with arbitrarily large data. The large-time behavior of solutions in the case of first-order kinetics has been recently studied. In this paper, we present new results concerning the case of higher-order kinetics for fairly general kinetics law (unbounded with respect to density and temperature, and dealing with the ignition phenomenon), including L2 and H1-stabilization rate bounds of power type. The power exponents of bounds improve essentially those known for related problems and are partially proved to be sharp. An effect of “faster equaling” of values in space for the concentration of unburned gas is also found. Finally we show how our results are modified in the case of reaction without diffusion.