Relation between gunpowder burning-rate responses to oscillating pressure and an oscillating radiant heat flux

In the linear approximation of the Zel'dovich–Novozhilov theory, we found an analytical relation between the response function to oscillating pressure, determined at a certain initial temperature, and the response function to oscillating radiant heat flux, determined at the same pressure but at another, lower, initial temperature. The difference between the initial temperatures satisfies the equality condition between the steady-state burning rates in the absence and in the presence of the radiant heat flux and is proportional to the latter.