Existence and stability of time-periodic solutions in a model for spherical flames with time-periodic heat losses

The problem under investigation is the study of the effect of periodicity when time-periodic heat losses are added in a model for spherical flames introduced by G. Joulin. In the present context, the flame either quenches in finite or infinite time, or its radius converges to an upper stable time-periodic solution, or to a lower unstable time-periodic solution.