Asymptotic stability of traveling waves in solid-propellant combustion under thermal radiation

The steady burning stability of solid propellants under thermal radiation with volumetric absorption is investigated. The combustion model we are dealing with includes the classical assumptions of quasiplanarity of all spatial variations, quasisteadiness of the gas phase and surface reaction. However, the stability analysis requires neither assuming a specific pyrolysis law nor formulating a specific flame submodel as long as the surface mass production and heat feedback satisfy some general properties, which are indeed observed experimentally. The existence of a steady state (traveling wave) solution is proved, and a dispersion relationship for its asymptotic stability is derived by conveniently transforming the problem into an evolution equation in a Banach space. The fully opaque burning surface limit and the case of transparent burning surface with exponential volumetric absorption are examined in details. The resulting stability regions in a proper parameter space are given and, finally, existence and stability of bifurcating time-periodic solutions are discussed.