On the equation of pulsating flame fronts in solid fuel combustion

A strongly nonlinear equation describing the dynamics of pulsations in solid fuel combustion is obtained. The method consists of extending the problem via introduction of an artificial parameter into boundary conditions leading to a separation of the spatial and the temporal scales within a low-frequency region. The interface dynamics equation obtained through an asymptotic expansion is then extrapolated toward the original values of parameters. The key point in the derivation is to restore the unexpected form of the principal nonlinearity generating a strongly dissipative region near a stagnation point of the front which is responsible for the stability of pulsations. The results of a numerical simulation of the equation demonstrate strongly relaxational stable oscillations of the flame front velocity.