For many regimes of SHS (solid-state combustion), dynamics of the deflagration front are determined by the subtle interaction between the energy release by the combustion process and energy dissipation by the media. Properties of a well-known mathematical model that captures basic mechanisms of this interaction will be discussed in the talk.
The simplest version of the model consists of two heat equations for the temperature in two semi-infinite domains ("cold" and "burnt" material), with three boundary conditions at the free boundary which represent the heat conservation and the kinetic relation between the temperature and the interface velocity. For a natural class of kinetic functions the model problem is well-posed globally in time, with uniformly bounded solutions. Numerical simulations on the model reveal an amazing variety of dynamical patterns, including sequences of period doubling bifurcations leading to chaos, infinite period bifurcations, spinning waves etc. Dynamics of a three-mode approximation by a system of ordinary differential equations will also be discussed.
This work is a joint work with Michael Frankel of Indiana University-Purdue University at Indianapolis.