Abstract
—The title problem for a spherical droplet is considered when the activation energy is large. Asymptotic solutions are obtained when the specific heat of vaporization is smaller than the heat of decomposition (otherwise there is no burning). The response curve of burning rate M versus Damköhler member D is C-shaped, thereby exhibiting auto ignition/extinction. At the top of the curve, M increases indefinitely with D while at the bottom there is a point beyond which M stays constant as D increases.